Mathematics - PearsonAccess.com

Mathematics Answer KeyThe height of the cylinder is equal to the lengthof the prism, 55 mm.V Bh 314 • 55 17,279 mm 3Volume of the prism Volume of the cylinder 37,950 17,279 20,671 mm 3The volume of metal used in each machine partis approximately 20,671 cubic millimeters.Question 80 (page 225)A Correct. Parallelogram ABCD has a base of4 units and a height of 2 units. The parallelogramwith coordinates (0, 2), (2, 2), (1, 1), and (1, 1)has a base of 2 units and a height of 1 unit. Since4 • 1 2 2 and 2 • 1 1, this parallelogram is a2dilation of parallelogram ABCD by a scale factorof 1 . The figures are similar.2Question 81 (page 226)B Correct. Since the stripe and the base of the sailare parallel lines, their corresponding angles areall equal. Thus, ABC is similar to DBEbecause their angles are equal in measure. Setup a proportion that relates BC to three knownmeasurements. DE corresponds to AC, and BEcorresponds to BC. D E B EAC BC 4 . 8 10 12B CUse cross products to solve for BC.4.8 • BC 12 • 104.8 • BC 120BC 25The length of BC is 25 feet. Subtract to find thelength of EC.BC BE EC25 10 EC15 ECThe distance from the bottom of the sail to thestripe is 15 feet.Question 82 (page 226)C Correct. The larger cube is a dilation of thesmaller cube. The surface area of the dilatedcube equals the square of the scale factormultiplied by the original surface area. The scalefactor of the dilation is 3, so the square of thescale factor is (3) 2 9. The surface area of thecube increases by a factor of 9.Question 83 (page 226)C Correct. ABC is similar to EDC. To find thelength of DC, write a proportion and solve forDC.In similar figures, corresponding sides areopposite congruent angles.AB corresponds to ED, and BC corresponds to DC.DC is 9 inches long.A B BC EDD C 2 0 1 512x20x 12 • 1520x 180 2 02 x0 1 802 0x 9Question 84 (page 226)A Correct.The formula for the volume of a cone is V 1 3 Bh,where B is the area of the base.The base of a cone is a circle, and the area of acircle is πr 2 . Substitute this expression for B inthe volume formula.V 1 3 πr2 hFind the volume of the sugar cone.Its radius, r, is 2 centimeters, and its height, h,is 15 centimeters.V 1 3 π(2)2 (15)V 20πV 62.83 cm 3Find the volume of the waffle cone. Its radiusis 3 times longer than the radius of the sugarcone. Since the radius of the sugar cone is2 centimeters, the radius of the waffle coneis 3 • 2 6 centimeters.Its height is 15 centimeters.V 1 3 π(6)2 (15)V 180π295