A Problem Solving Approach to Mathematics for Elementary School Teachers (13th Edition)

Chapter 13

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; Divide the given circle into 4 parts by drawing... more

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Ratio is approximately .Average is approximately .... more

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All metric units of length are related to the base... more

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Since and is 5 times , multiply 5 by 1,000 to ... more

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; Use   to convert   into centimeter,Use   to ... more

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        ; Substitute for into the formula of ... more

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The circumference of the circle gets doubled.  ; ... more

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; The length of an arc of a circle of radius   is... more

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; Let the radii of the circles be ,  , and . ... more

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; Use the conversion .Convert   into centimeter.... more

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; Circumference is the distance around the circle... more

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To explain the reason because of which triangle ... more

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The radius of the circle gets doubled. ; The ... more

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; The length of an arc of a circle of radius   is... more

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; Let the radii of the circles be ,  , and . ... more

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Runners must complete the lap of the track from ... more

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Centimeter because it is a small measurement unit... more

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The required ratio is .The length of the arc of a ... more

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If the diameter of the larger semicircle is , then... more

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The spot on Object W touches the sidewalk 8 times.... more

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Triples can be used: 1, 1, and 1; 2, 2, and 1.... more

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Observation and research show that the size of ... more

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The circumference of Container C is greater as ... more

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To make the calculation easier, sometimes is used... more

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Yes, because the wire will be approximately above... more

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YesLet the length of the diameter be and the ... more

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No; There are 1000 meters in 1 kilometres, so 5 ... more

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Millimetersare used for the measurement of very ... more

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Person F's rope is 12 inches long, and it is ... more

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; The circumference of a circle is given by , ... more

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; Let   be the side of the first square and   be ... more

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The area of the triangle, that is , can be ... more

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The parallelogram is transformed into a rectangle... more

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YesThe area of the rectangle will be decreased by... more

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The resultant figure will be a parallelogram and ... more

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Person A is of the opinion that the area of a ... more

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This is not true as a thread of the same length ... more

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No, it is not possible to find the area of a thing... more

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"are" and "hectare" are the units of area, so it ... more

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The claim of Person D is not correct since it is ... more

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The formula of the area of a rectangle is the ... more

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; A quadrilateral with its diagonal perpendicular... more

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A:  B:  Total area:  Area of Object C:   ; The ... more

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; The circumference for an arc with angle   is  .... more

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; Redraw the figure with label of measure of ... more

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; The length of arc of the sector is given by the... more

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Estimated Area: ; Actual area:  Difference in the ... more

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Area would be same in both the cases. ; If the ... more

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Total area: ;Area of Object C: square feet ; The ... more

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A composite shape is made up of simple geometric ... more

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Estimate area of appliance D: 6 times the area of ... more

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; As described, draw the triangle inside the ... more

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; Assume that   is a constant. Then, the side of ... more

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To find the area of a parallelogram, its base ... more

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; A rhombus is in the shape of a kite, with all ... more

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; It is given that .Multiply   and   by 100 ... more

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; The area of a circle is , where   is the radius... more

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; The area of the shaded region is obtained by ... more

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; The area of a circle is , where   is the radius... more

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; Area of a triangle is , where   is base and   ... more

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; The area of a circle is , where   is the radius... more

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; The area of a sector with radius   is .... more

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; The area of a parallelogram is , where   is the... more

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; The area of a trapezium with base   and , and ... more

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; In a regular hexagon, the side is equal to the ... more

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The estimated area is of 3 hands and the actual ... more

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Entire Proof Answer: From the figure in part 6(a... more

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The third vertex of the triangle will be outside ... more

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; It is known that  Multiply   by   to convert it... more

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; The area of a rectangle is , where   is the ... more

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; The area of a rectangle is  , where   is the ... more

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The circular Object P inside the square has less ... more

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The areas of the inside and the outside of the ... more

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; The area of the square is  , where   is the ... more

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; Label each region of the given figure. ; Let ... more

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Determine the area of four small rectangles which ... more

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First pack ; The area of a rectangle is  , where... more

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; Rotate square   along the center of square   ... more

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The area of   is 9 times of the area of . ; When ... more

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; The area of a circle is  , where   is the ... more

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; The radius of the circle   is half of its ... more

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; The area of a sector with radius   is  .... more

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; The area of a trapezium with base   and , and ... more

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; In a regular hexagon, the side is equal to the ... more

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180 ; The area of a rectangle with length   and ... more

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The area of a triangle is , where   is the base ... more

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; The area of a rectangle with length   and width... more

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The perimeter of a rectangle with length   and ... more

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There are about 48 squares in the shaded region.... more

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In a right triangle, the sum of squares of lengths... more

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Consider a with side lengths , , and , where is ... more

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According to the Pythagorean Theorem, , where and... more

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As , the given triangle is not a right triangle... more

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A geometric proof is based on reason, logic, and ... more

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The converse of Pythagorean Theorem states that if... more

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The coordinates of two points on the -plane are ... more

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; Let the vertical and horizontal distances ... more

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units ; Let the vertical and horizontal distances... more

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; Let the length of the smaller leg of the given ... more

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; Assume that the length of the diagonal of a ... more

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; Use the coordinate axes to plot the route of ... more

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; As the surface and object W are perpendicular, ... more

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; Label the given trapezium as , and draw a ... more

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; The measurements made by the company are the ... more

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Entire Proof Answer:Each side of the quadrilateral... more

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; Join the centers of the circles with a line ... more

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unitsAccording to   triangle relationship, the ... more

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; Draw the right-angled triangle which shows the ... more

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; The diagonals of a rhombus bisect each other at... more

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Entire Proof Answer: The triangles similar to the ... more

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If a polygon has interior vertices, then its ... more

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Use the conversion   to convert the length of ... more

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; As, a right-angle triangle is formed with the ... more

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; The circle formed by the range has centre and ... more

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; As a right-angle triangle is formed by the ... more

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to the nearest ; Mark the point   in the diagram... more

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; Divide the length of   by 2 to find the length ... more

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; Observe the home base, first base, and third ... more

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Entire Proof Answer: It is given that , which ... more

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In the given figure, the outside quadrilateral is ... more

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Entire Proof Answer: Area of a circle can be ... more

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; Substitute 0 for  , 0 for  ,  for , and   for... more

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Entire Proof Answer: Calculate the lengths of all ... more

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or ; Plot the given triangle having   as the ... more

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; Let   be the inner circle having the first ... more

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; The tangent   touches the circle at point .... more

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; Two diagonals divide the rhombus into four ... more

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Entire Proof Answer: Let , , and be the three ... more

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Entire Proof Answer: Let   and   represent the ... more

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Join   and . Draw a perpendicular from   to the ... more

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Let the lengths of the sides of the right triangle... more

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Draw a right triangle with two legs of the lengths... more

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Entire Proof Answer: Determine the areas of the ... more

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The area of the   can be found by adding the areas... more

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Approximately To find the area between the given ... more

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Entire Proof Answer: Assume a right triangle with... more

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Individual J made a mistake by taking addition of ... more

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Square rod is a unit that is used to measure the ... more

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Individual S got a good deal than Individual M as ... more

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; The coin of the given currency of Country U has... more

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The measures of the hypotenuse, base, and ... more

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When the figure will be folded from the dashed ... more

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; Substitute 6 for , for , and 4 for   into the ... more

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; Since , convert the given radius and height ... more

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; Substitute 6370 for into the formula   to find... more

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; Substitute 4 for into the formula . ; Simplify... more

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; Draw a right triangle inside the hexagon such ... more

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; The can is in the shape of a right circular ... more

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; Let length, width and height be , and of the ... more

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; Take the square root of the given area to find ... more

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; Substitute for into to find the ... more

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; Let and be the length and radius of the first... more

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; Divide the diameter by 2 to find the radius. ; ... more

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; Let and be the edges of the first and the ... more

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; Substitute 10 for , for , and for into the ... more

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; There are 6 faces in a hexagonal prism.Multiply... more

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; Convert the dimensions given in the feet into ... more

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In the given figure, there are 4 rectangles and 2 ... more

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; Area of a rectangle is given by , where   is ... more

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; The height, slant height and half of the base ... more

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; The lateral surface area of the right circular ... more

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; Calculate the base,  , from the area of the ... more

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Calculate the surface area with as and as .As ... more

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; Let   be the length of the first cone and   be ... more

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The surface area of planet J will be 121 times as ... more

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; Calculate the surface area of the first cube by... more

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; Calculate the surface area of the outer cube ... more

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; Dissect the figure to show the cross-section... more

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; Find the slant height as the height of ... more

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Substitute for into to find the surface area of... more

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No effectThis is because there is a loss of and a... more

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Entire Proof Answer: For the given result to be ... more

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; Draw a labeled right circular cone containing ... more

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Radius: ;Find the circumference of the given ... more

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; Substitute for , for , and for into the ... more

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; Consider a right triangular prism with the ... more

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No; the person needs nine times of the previous ... more

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Person G is not correct because the surface area ... more

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YesThe formula used by Person A is in factored ... more

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Person J is wrong as four times the previous ... more

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Person R is wrong because the surface area of ... more

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; Let and denote length and width of the ... more

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; As the diagonals of the rhombus bisect each ... more

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; Use the Pythagorean theorem on triangle to ... more

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; The diagonal of a cube is given by , where ... more

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Consider a circular ring of any radius. The given ... more

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The given prism has five faces.The figure given in... more

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If heights and radii of a cone and a cylinder are ... more

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 The required volume is about cubic inches. ; The... more

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Multiply the volume of the cone by 3. ; Let the ... more

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; Calculate the number of drops in 30 days by ... more

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; The given Structure GP is similar in shape with... more

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  ; For (a), the given value is . Use the ... more

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; Substitute 4 for , 4 for , 4 for , and   for   ... more

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It becomes 8 times the volume of the original ... more

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 (a)(b)(c)(d) ; The volume of a rectangular prism ... more

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; If the diameter of a sphere is   times the ... more

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; Substitute 50 for , 25 for , and 2 for   into ... more

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; Object S is cylindrical.If the diameter is 4 mm... more

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Great pyramid Ch has approximately   times greater... more

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; Let   be the height and   be the radius of the ... more

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; Let   be the side of the given cube. Then, the ... more

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; Find the volume of one Object B by substituting... more

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; The shape of Object C is cylindrical. So, the ... more

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The volume of prism is equal to the volume of ... more

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To measure the weight of heavy objects, the unit ... more

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The given object cannot have a mass of 340 grams ... more

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; The mass of water in the tank is equal to the ... more

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; There are approximately   grams in a pound.The ... more

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Fish AG:  Fish C:   ; Convert   to English ton by ... more

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; Find the weight of the single sheet by dividing... more

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; Convert the width of the floor, , to inches ... more

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; Use the conversion   to convert the required ... more

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; The volume of the stones is equal to the ... more

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; Find the increase in the height by subtracting... more

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  ; For (a), the given value is . Use the ... more

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27 times of the volume of the original sphere ; ... more

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  ; The volume of a rectangular prism is given by... more

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Larger Fruit M; At the price of   times of the ... more

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; The given figure is made of two prisms. One is ... more

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; Find the radius, , when the diameter is using ... more

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; Find the outer radius by adding and .Convert ... more

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No, the amount of Item P reduces to one-third for ... more

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; It is known that .The volume of a cylinder is ... more

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Second Item F ; Substitute for , for , and for... more

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; First, find the volume of sphere by ... more

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; Let the edge of the box be . So, the volume of ... more

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About times the radius of the original Object B... more

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; Observe that a square of size   has been cut ... more

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To measure the weight of light objects, the unit ... more

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To measure the weight of light objects, the unit ... more

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; There are approximately   grams in a pound.The ... more

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Fish AG:  Fish C:   ; Convert   into kilograms by ... more

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; Find the weight of the single sheet by dividing... more

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; Convert the width of the floor, , to inches ... more

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; Use the conversion   to convert one kilogram ... more

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The volume of an irregular shape can be found by ... more

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The second problem is easier because the ... more

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The feasibility can be justified by the fact that ... more

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Any box can be used because the length of the ... more

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; The diagonal of a cube is the hypotenuse of the... more

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; The volume of cylinder is , where is the ... more

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A box of length , width , and height is the one ... more

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Design a cylinder having a radius of and a height... more

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Yes because weight depends on density that depends... more

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Yes, the volume and the surface area of a cube can... more

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The volume of cube is not . Students do not ... more

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Person A is right as the volume will be increased ... more

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The choice of Person B was wrong because she had a... more

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Yes, any cube is similar to another cube and any ... more

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; Use the Pythagorean theorem to determine the ... more

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The length of the nonface diagonal is more because... more

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The total available volume is very small, and it ... more

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The given unit is used to measure the area of ... more

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The diameter of the cylinder is , which implies ... more

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; Convert the diagonal of the rectangle into   ... more

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; The circumference   of a circle with radius   ... more

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Individual M is incorrect because the ... more

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The area of the rectangle in the given second ... more

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Since the base of all the triangles is same, the ... more

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; Reconstruct the diagram and determine the height... more

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; Find the length   of the right triangle   using... more

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; Surface area is the sum of areas of all sides ... more

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; Find the lateral side,  , of the right circular... more

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The year 2020 figure shows that company’s growth ... more

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; The area of a kite with diagonals and is ... more

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; Convert the value of the diagonal of the ... more

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; The area of a triangle with base and height ... more

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Width:   ; Using the given information, draw the ... more

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; The formula for the volume of cylinder is and ... more

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; The length and width of the cut of a rectangle ... more

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; The capacity of sphere is the volume of the ... more

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; Using similarity principle, if two similar ... more

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In both plans, the area covered by Object S is the... more

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Entire proof answer: Side is equal to side ... more

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