a.

694.4

c.

90.0

b.

1,157.4

d.

54.0

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