The surface area of two similar solids are 384 yd² and 1,057 yd². The volume of the larger solid is 1,796 yd³. What is the volume of the smaller solid?

a. 1,795 yd²
b. 1,082 yd²
c. 393 yd²
d. 978 yd²

1 answer

Since the solids are similar, the ratio of their surface areas is equal to the square of the ratio of their lengths. Let x be the ratio of the lengths. Then we have:

(x²)384 = 1,057

Solving for x, we get:

x = √(1,057/384) ≈ 1.5

So the lengths of the two solids are in a 1:1.5 ratio. Since the volume is proportional to the cube of the length, the ratio of the volumes is:

(1.5³) = 3.375

So the volume of the smaller solid is:

1,796/3.375 ≈ 532 yd³

Therefore, the answer is not among the choices given.