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?

Respuesta :

Answer:

It depends on the relation between the heights  of both pyramids

Step-by-step explanation:

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

[tex]V=\frac{1}{3}bh[/tex]

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

[tex]\frac{1}{3}b_ah_a=3*\frac{1}{3}b_bh_b=b_bh_b[/tex]

Which means

[tex]b_ah_a=3*b_bh_b[/tex]

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

[tex]b_a=3*b_b[/tex]

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

[tex]3*b_a=3*b_b=>b_a=b_b[/tex]

Both bases would be the same.

If we choose that  

[tex]h_a >3*h_b[/tex]

it would mean

[tex]b_a<b_b[/tex]

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