Answer:
The volume of P is 1728 cubic yards.
Step-by-step explanation:
For similar shapes, the ratio of volumes are defined as:
[tex]\frac{V_{1} }{V_{2}}[/tex] = [tex](\frac{h_{1} }{h_{2}}) ^{3}[/tex]
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:
[tex]\frac{V_{P} }{V_{Q}}[/tex] = [tex](\frac{h_{P} }{h_{Q}}) ^{3}[/tex]
[tex]\frac{V_{P} }{8}[/tex] = [tex](\frac{6}{1} )^{3}[/tex]
Vp = 6³ * 8
= 216 * 8
Vp = 1728 cubic yards
The volume of P is 1728 cubic yards.
