Question

The volume of two similar solids is 1331 m3 and 729 m3. The surface area of the larger solid is 605 m2.

What is the surface area, in square meters, of the smaller solid?
Explanation and answer please or just answer :)

Answer 1

If 2 solids have a scale factor of s for their linear dimensions (side lengths, radii, etc.), then their surface areas have a scale factor of \(s^2\), and their volumes have a scale factor of \(s^3\).

The problem tells you the volume scale factor is

\(\dfrac{1331}{729} \), so

\(s^3 = \dfrac{1331}{729} \)

Take the cubic root of each side to find s, the linear scale factor.
Then square each side to find \(s^2\), the area scale factor.
Then divide the surface area of the larger solid by the area scale factor to find the surface area of the smaller solid.
.