Question

The square pyramid has a volume of 27 cubic inches. What is the value of X?

It has a height of 1/9x in. Please help

Answer 1

9 inches

Explanation:

base is rectangular in shape

Side of base of square pyramid is X inches

height of square pyramid is 1/9 X

Volume of any pyramid is 1/3 *(area of base* height of pyramid)

area of base of square pyramid = Side of base * Side of base

as area of square is equal to side * side

area of base of square pyramid = x* x square inches =
`x^2 sq.\ inches`

Volume of pyramid = 1/3 *(area of base* height of pyramid)

substituting given value of of volume of pyramid , height of pyramid and area of base calculated above we have

`27 = 1/3(x^2)*(1/9 x)\\\\27*3*9 = x^3\\729 = x^3\\x = \sqrt[3]{729} \\x = 9`

Therefor value of x is 9 inches.