Word Problems

Question

An open rectangular box (no top) with volume 9 cubic meters has a square base. Express the surface area S of the box as a function of the length x of one of the sides.

 

s(x)=?

Answer 1

 

I would start this problem using 2 variables,,,,x as the side of the square base and y as the height.

The volume formula for a rectangular solid is V = l*w*h so in you case you can write the equation

 

9 = x^2 * y so y = 9/(x^2)

 

The surface area is founs by adding up the area of the 5 faces, since there is no top.

so SA = x^2 + 4xy. But the problem is asking as a function of x only. That's where the first equation comes in

 

s(x) = x^2 + 4x*( 9/(x^2) ) 

s(x) = x^2 + 36/x when simplified.

Hope this helped.