Question

You have 132 cubic inches of clay, and you want to make a sculpture in the shape of a pyramid with a square base and a height that is 5 inches more than each side of the base (vpyramid=1/3l*w*h)

Answer 1

Given:

The volume of the pyramid with a square base is 132 cubic inches.

Height is 5 inches more than each side of the base.

Let x be the length of the side.

Since, it is square base,

Therefore, length= width= x.

Height is x+5.

Using the volume of pyramid formula,

$\begin{gathered} V=\frac{1}{3}\times l\times w\times h \\ 132=\frac{1}{3}\times x\times x\times(x+5) \\ 396=x^3+5x^2 \\ x^3+5x^2-396=0 \\ (x-6)(x^2+11x+66)=0 \end{gathered}$

Solving we get,

$x=6,\: x=-\frac{11}{2}+i\frac{\sqrt{143}}{2},\: x=-\frac{11}{2}-i\frac{\sqrt{143}}{2}$

Distance must not be in imaginary value.

Hence, the length is 6 inches and the width is 6 inches.

And the height is,

6+5=11 inches.

Therefore, l=6 inches, w=6 inches, and h=11 inches.