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?

Question

a. 1,795 yd³
b. 1,082 yd³
c. 393 yd³
d. 978 yd³

Answer 1

We know that the ratio of surface areas is the square of the ratio of lengths of corresponding sides, and the ratio of volumes is the cube of the ratio of lengths of corresponding sides. Let x be the ratio of lengths of corresponding sides (i.e. the scale factor) between the smaller and larger solids.

Then we have:

(x²) * 384 = 1057
x = √(1057/384) ≈ 1.446

And:

(x³) * V = 1796
V = 1796 / (x³) = 1796 / (1.446³) ≈ 1082

So the volume of the smaller solid is approximately 1082 yd³, which is choice (b).