Question

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


The pyramids must have the same base shape.

The pyramids must have the same slant height.

The areas of the bases must be the same.

The pyramids must be identical in size and shape.

Answer 1

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

Answer 2

The true statement is (c) The areas of the bases must be the same.

The volume of a pyramid is calculated as:

$V = Bh$

Where:

B represents the base area

h represents the height

V represents the volume

When the volume and the height of both pyramids are equal, then the base area must be the same

Hence, the true statement is (c) The areas of the bases must be the same.

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