Question: What is the ratio of the surface area of the square prism to the surface area of the rectangular prism?

A ) 2 : 3
B ) 1 : 2
C ) 3 : 5
D ) 2 : 5

Steps to derive

1 Surface area of the square prism = 6 × (edge)² = 6 × 10² = 600 cm.²

2 Dimensions of the rectangular prism are 30 cm. × 10 cm. × 5 cm.

3 Surface area of the rectangular prism = 2(lw + wh + lh)
 [Formula.]

 [Substitute.]
4 = 2((30 × 10) + (10 × 5) + (30 × 5))

 [Multiply.]
5 = 1000

6 Surface area of the rectangular prism = 1000 cm.²

7 Ratio of the surface area of the square prism to the surface area of the rectangular prism = 600 : 1000
= 3 : 5
 [Simplify.]

8 The ratio of the surface area of the square prism to the surface area of the rectangular prism = 3 : 5



Hence the right answer is Option C

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