SOLUTION: The figure shows an open box with a square base. The box is to have a volume of ten cubic feet. Express the amount of material needed to construct the box, A as a function of the l

Algebra ->  Functions -> SOLUTION: The figure shows an open box with a square base. The box is to have a volume of ten cubic feet. Express the amount of material needed to construct the box, A as a function of the l      Log On


   

Question 1044299: The figure shows an open box with a square base. The box is to have a volume of ten cubic feet. Express the amount of material needed to construct the box, A as a function of the length of a side of its square base,x.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x edge of square base
y height of the open box

x%5E2y=10 accounts for volume.

Amount of material , S, is sum of all the five surface areas.
4xy%2Bx%5E2=S

Solve the volume equation for y.
y=10%2Fx%5E2
Substitute into the S equation.
S=4x%2810%2Fx%5E2%29%2Bx%5E2
Simplify.
S=%2840%2Fx%2B4x%5E3%29
S=40%2Fx%2B4x%5E4%2Fx
highlight%28S=%2840%2Bx%5E4%29%2Fx%29