SOLUTION: A rectangular box with a square base has surface area 52 in2. Find a function that models the volume of the box in terms of the length x of one side of its base.

Algebra ->  Functions -> SOLUTION: A rectangular box with a square base has surface area 52 in2. Find a function that models the volume of the box in terms of the length x of one side of its base.      Log On


   

Question 1061434: A rectangular box with a square base has surface area 52 in2. Find a function that models the volume of the box in terms of the length x of one side of its base.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x and x bottom dimensions;
y, the height dimension;

x%5E2%2Bx%5E2%2B4xy=52
2x%5E2%2B4xy=52

VOLUME for the box, v is
v=yx%5E2


Solve the area equation for y in terms of x.
4xy=52-2x%5E2
2xy=26-x%5E2
y=%2826-x%5E2%29%2F%282x%29

Substitute this for y in the volume equation.
v=%28%2826-x%5E2%29%2F%282x%29%29x%5E2
v=%28%2826-x%5E2%29x%5E2%29%2F%282x%29
v=%28%2826-x%5E2%29x%29%2F2
highlight%28v=13x-%281%2F2%29x%5E3%29