A closed box is to be made in the shape of a cubiod, of height h cm and with a square base that has sides of length x cm.

Question

Its volume V is required to be 500 cm^3.

A) write an expression for the V (volume)in terms of h and x.

B)Write an expression for the surface area A in terms of h and x. use the result for A) to write A in terms of x only.

C) Use differentiation to determine the value of x which has A as a minumum. What is the coresponding value of h?

Answer 1

x^2h=500, so h = 500/x^2

v = x^2h
A = x^2 + 4xh = x^2 + 2000/x
dA/dx = 2x - 2000/x^2 = 2x(x^2-1000)/x^2