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:

$volume = \frac{l \times w \times h}{3}$

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,

$81 = \frac{3h \times 3h \times h}{3}\\\\81 = 3h^3\\\\h^3 = 27\\\\\text{Take cube root on both sides }\\\\h = \sqrt[3]{27} \\\\h = \sqrt[3]{3 \times 3 \times 3} = \sqrt[3]{3^3} \\\\h = 3$

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