6
AssignmentMultiple Choice

Changing Dimensions of 3-D Figures

Question 6 • (OC27) GEO-1206310-S2-Degele-VOL7006P

The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74.32 inches2, what is the surface area of the larger solid? Round to the nearest hundredth.

Answer
A
133.78 in.2
B
240.80 in.2
C
433.43 in.2
D
678.32 in.2

Explanation

For similar solids, the ratio of their volumes is the cube of the scale factor. Since 729/125 = (9/5)³, the surface-area scale factor is (9/5)² = 3.24. Multiply the smaller surface area by 3.24: 74.32 × 3.24 = 240.7968, which rounds to 240.80 in.², choice B.

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