Question

An open top box with a square base is to have a volume of 350 cubic meters. The material for the bottom of the box costs $2 per square meter and the material for the sides costs $6 per square meter. Write an expression that represents the cost of constructing the box in term of x, the side length of the base.

Answer 1

Answer:$C=2x^2+\frac{8400}{x}$

Step-by-step explanation:

Given

Volume of box $V=350\ m^3$

Suppose base square has a length $x\ m$

and vertical walls has length of $y\ m$

volume $V=x^2y$

$y=\frac{350}{x^2}$

Cost of bottom material $=\ 2$ per square meter

Cost of side material $=\ 6$ per square meter

Total cost

$C=x^2 \times 2+4xy\times 6$

$C=2x^2+4x\times \frac{350}{x^2}\times 6$

$C=2x^2+\frac{8400}{x}$