Question

if the volume of the pyramid is 81 in cubed, and l equals w equals 3 h, what is the length of the base of the pyramid in inches?

Answer 1

The length of the base of the pyramid is 9 inches

Solution:

The volume of pyramid is given by formula:

`volume = (l * w * h)/(3)`

Where, "l" is the length and "w" is the width and "h" is the height

Given that,

volume of pyramid = 81 cubic inches

Also given that, l equals w equals 3 h

l = w = 3h

Substitute the values in formula,

`81 = (3h * 3h * h)/(3)\\\\81 = 3h^3\\\\h^3 = 27\\\\\text{Take cube root on both sides }\\\\h = \sqrt[3]{27} \\\\h = \sqrt[3]{3 * 3 * 3} = \sqrt[3]{3^3} \\\\h = 3`

Thus height = 3 inches

We have to find the length

l = 3h

l = 3(3) = 9

Thus length of the base of the pyramid is 9 inches