Question

P and Q are similar hexagonal pyramids. The scale factor of P to Q is 6 : 1. If the volume of Q is 8 cubic yards, find the volume of P.

Answer 1

The volume of P is 1728 cubic yards.

Explanation:

For similar shapes, the ratio of volumes are defined as:

`(V_(1) )/(V_(2))` =
`((h_(1) )/(h_(2))) ^(3)`

where h1 and h2 are the heights of each pyramid respectively.

We know that the scale factor of P to Q is 6:1 i.e. the ratio of heights is also 6:1. And the volume of Q is given as 8 cubic yards. so, using the relation defined above we can write:

`(V_(P) )/(V_(Q))` =
`((h_(P) )/(h_(Q))) ^(3)`

`(V_(P) )/(8)` =
`((6)/(1) )^(3)`

Vp = 6³ * 8

= 216 * 8

Vp = 1728 cubic yards

The volume of P is 1728 cubic yards.