Question

If two pyramids have the same height, what must be true of the pyramids for them to also have the same volume?

Answer 1

The area of the bases must be the same. I just got it correct on the quiz.

Answer 2

Answer:

The answer is the option

The areas of the bases must be the same

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the base of the pyramid

h is the height of the pyramid

In this problem we have

Pyramid N 1

$h1=h\ units$

$B=B1\ units^{2}$

Substitute

$V1=\frac{1}{3}B1h$

Pyramid N 2

$h2=h\ units$

$B=B2\ units^{2}$

Substitute

$V2=\frac{1}{3}B2h$

Remember that

the two pyramids have the same volume

so

$V1=V2$

$\frac{1}{3}B1h=\frac{1}{3}B2h$

$B1=B2$

therefore

The areas of the bases must be the same