Question

The formula of the volume of a pyramid is 1/3BH, where B represents the area of the base of the pyramid and H represents the height of the pyramid. The volume of pyramid A is 3 times the volume of pyramid B. Is the area of the base of Pyramid A greater, equal, or less that the area of the base of Pyramid B?

Answer 1

It depends on the relation between the heights of both pyramids

Explanation:

We know the volume of a pyramid of base b and height h is

`V=(1)/(3)bh`

If the volume of the pyramid A is 3 times the volume of the pyramid B, then

`(1)/(3)b_ah_a=3*(1)/(3)b_bh_b=b_bh_b`

Which means

`b_ah_a=3*b_bh_b`

If we knew both heights are the same, we could conclude that

`b_a=3*b_b`

In which case the base of the pyramid A would be greater than the other base

But if, for example, the height of the pyramid A is 3 times the height of the other height, then

`3*b_a=3*b_b=>b_a=b_b`

Both bases would be the same.

If we choose that

`h_a >3*h_b`

it would mean

`b_a<b_b`

In which case the base of the pyramid A would be less than the other base

So the answer entirely depends on the relation between the heights of both pyramids