Question

The square pyramid has a volume of 486 cubic inches. What is the value of x?

Answer 1

Volume of square pyramid can be calculated by the formula :

V=$a^{2}\frac{h}{3}$

a is the length of base and h is the height of the pyramid.

In the given figure a= x in.and h = $\frac{1}{4} x$ in.

Volume of pyramid given V =486 cubic inches.

Substituting these values in volume of pyramid we have:

486= $x^{2} \frac{x}{4}$ ÷ 3

Or 486=$\frac{x^{3}}{4} x\frac{1}{3}$

486= $\frac{x^{3}}{12}$

Multiplying both sides by 12

5832 =$x^{3}$

$18^{3} =x^{3}$

Or x= 18 in.

Answer 2

Base Length = 18
Base Width = 18
Heigth = 4.5
x = 18

Hope this helpz!