Question

The dimensions of a small pyramid are one-third the dimensions of a larger

pyramid. If the volume of the larger pyramid is 810 cm³, what is the volume of

the smaller pyramid?

Answer 1

30 cm³

Explanation:

You want the volume of a small pyramid similar to a larger one of volume 810 cm³ if the scale factor is 1/3.

Scale factor

The scale factor for volume is the cube of the scale factor of the linear dimensions:

volume scale factor = (1/3)³ = 1/27

Volume

The volume of the smaller pyramid is that of the larger pyramid multiplied by the volume scale factor:

(810 cm³) × (1/27) = 30 cm³

The volume of the smaller pyramid is 30 cm³.