The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74.32 inches2, what is the surface area of the larger solid? Round to the nearest hundredth.

This is the concept of scales factors, given that two similar solids with 729 inches^3 and 125 inches^3. The volume scale factor will be given by:

(volume of larger solid) / (volume of smaller solid)

=729/125

but

linear scale factor = (volume scale factor) ^1/3

thus the linear scale factor will be:

(729/125) ^1/3

=9/5

Also, area scale factor will be given by:

area scale factor = (linear scale factor) ^2

= (9/5) ^2

=81/25

The area of the larger solid will be given by:

let the area be A;

A/74.32=81/25

thus

A=81/25*74.32

A=240.7968 inches^2