Question

A pyramid has a square base of side x (in cm), and a height h (in cm) and its volume V is given by the formula V = 1/3x^2h. If the sum of the length of the base side and the height is 9, find the max volume. Give the dimensions of maximum volume.

Answer 1

so what is the problem?

Answer 2

length=x
x+h=9
\[V(x)=\frac{x^2h}{3}=\frac{x^2(9-x)}{3}=\dfrac{9x^2-x^3}{3}\]
find
\[V'(x)=0\]
x=is the dimention