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Katyanochek1 [597]
3 years ago
7

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 volum

e of P.
Mathematics
1 answer:
tatiyna3 years ago
8 0

Answer:

The volume of P is <u>1728 cubic yards.</u>

<u></u>

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 <u>1728 cubic yards.</u>

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