Question

Two similar pyramids have lateral areas 8ft^2 and 18 ft^2. the volume of the large pyramid is 108 ft^2. find the volume of the smaller pyramid.

Answer 1

I assume the volume of the larger pyramid is 108 ft^3, not 108 ft^2.

The scale factor of edges of two solids is x.
The scale factor of their areas is x^2.
The scale factor of their volumes is x^3

The areas have a scale factor of 18/8 = 2.25

The length have a scale factor of sqrt(2.25) = 1.5

The volumes have a scale factor of 3.375

108/3.375 = 32

Answer: 32 ft^3