Question

A pyramid and a cone are both 10 centimeters tall and have the same volume. What state must be true about the two solids

Answer 1

Tbase area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

Explanation:

Points to remember

Volume of pyramid = (a²h)/3

Where a - side of base

h - height of pyramid

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the correct answer

We have height of pyramid and cone is 10 cm

(a²h)/3 = (πr²h)/3

(a² * 10)/3 = (πr² * 10)/3

10a² = 10πr²

From this we get base area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

Answer 2

The horizontal cross-sections of the pyramid and the cone at the same height must have the same area.

Explanation:

We are given that a pyramid and a cone are both 10 centimeters tall and have the same volume and we are to determine a statement which must be true for both the solids.

The horizontal cross-sections of the pyramid and cone at the same height must have the same area.

This is because