Question

A pyramid has the same volume as a cube of side 10.0 cm

The height of the pyramid is the same as the side of the square base

Calculate the height of the pyramid

Textbook says the answer is 14.4 cm but i don't understand how

Please explain with step by step explanation

Answer 1

The height of the pyramid is 14.4 cm.

How to find the height of the pyramid?

volume of a pyramid = 1 / 3 Bh

where

• B = base area
• h = height of the pyramid

Therefore,

volume of the cube = L³

where

• L = side length of the cube

Hence,

volume of the cube = 10³

volume of the cube = 1000 cm³

The volume of the pyramid is the same with the  volume of the cube.

Hence,

1000 = 1 / 3 Bh

The height of the pyramid is the same as the square base.

Therefore,

1000 = 1 / 3 (h²)h

1000 = 1  / 3 h³

cross multiply

3000 = h³

h = ∛3000

h = 14.4224957031

Hence, the height of the pyramid is 14.4 cm.

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