Volume of square pyramid can be calculated by the formula :
V=[tex] a^{2}\frac{h}{3} [/tex]
a is the length of base and h is the height of the pyramid.
In the given figure a= x in.and h = [tex] \frac{1}{4} x [/tex] in.
Volume of pyramid given V =486 cubic inches.
Substituting these values in volume of pyramid we have:
486= [tex] x^{2} \frac{x}{4} [/tex] ÷ 3
Or 486=[tex] \frac{x^{3}}{4} x\frac{1}{3} [/tex]
486= [tex] \frac{x^{3}}{12} [/tex]
Multiplying both sides by 12
5832 =[tex] x^{3} [/tex]
[tex] 18^{3} =x^{3} [/tex]
Or x= 18 in.
