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# The volumes of 2 similar solids are 27 and 125 . The surface area of the larger solid is 250 . What is the surface area of the smaller solid? Round your answer

a.
694.4
c.
90.0
b.
1,157.4
d.
54.0

### 1 Answer by Expert Tutors

Jose M. | Patient, Experienced Math and Science Tutor (MIT Grad)Patient, Experienced Math and Science Tu...
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1

When working with similar solids, what we care about are ratios. The following two equations are always valid for similar solids:

1. The ratio of the surface areas is equal to the square of the ratio of their corresponding linear measures

S_A/S_B = (a/b)2                       (1)

2. The ratio of the volumes is equal to the cube of the ratio of their corresponding linear measures

V_A/V_B = (a/b)3                       (2)

Plugging in the given information into equation (2) gives

27/125 = (a/b)3

If we then take the cubed root of both sides, we get

3/5 = a/b

Plugging this result into equation (1) along with the given information, we get

S_A/250 = (3/5)2

Multiplying both sides by 250 gives

S_A = 250*(3/5)2 = 250*(9/25) = 90