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

Answer:

The volume of P is 1728 cubic yards.

Step-by-step explanation:

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

$\frac{V_{1} }{V_{2}}$ = $(\frac{h_{1} }{h_{2}}) ^{3}$

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:

$\frac{V_{P} }{V_{Q}}$ = $(\frac{h_{P} }{h_{Q}}) ^{3}$

$\frac{V_{P} }{8}$ = $(\frac{6}{1} )^{3}$

Vp = 6³ * 8

     = 216 * 8

Vp = 1728 cubic yards

The volume of P is 1728 cubic yards.