The volumes of two similar solids are 216 ft ^3 and 1331 ft ^3. The surface area of the smaller solid is 180 ft ^2. What is the surface area of the larger solid?

Answer 1

Let x be the scale factor between the two similar solids.

Since volume is proportional to the cube of the scale factor, we have:

(216 / 1331) = (x)^3
x = (216 / 1331)^(1/3)
x ≈ 0.6

The surface area of the larger solid is equal to x^2 times the surface area of the smaller solid, so:

Surface area of larger solid = (0.6)^2 * 180
Surface area of the larger solid ≈ 64.8 ft^2

Therefore, the surface area of the larger solid is approximately 64.8 ft^2.