Question

A box has a square bottom and top and is 5 cm high. find its volume if its total surface area is 192cm2

Answer 1

Alright let's start by noting that due to it having a square bottom and top the Length is equal to the Width. They gave us the surface area, but what we need is the length/width of the square top/bottom. So let's take the surface area and make it equal to the equation for the surface area of a rectangular prism (our shape):

192cm^2 = 2(lw + lh + hw)

Let's replace all the "l's" with w's (we can do this due to the fact that the length (l) equals the width (w) (l = w)) 

192cm^2 = 2(w*w + wh + hw) 

192cm^2 = 2(w^2 + 2wh)

We know what the height (h) is as it is given in the problem (5cm).
192cm^2 = 2(w^2 + 2*5w)
192cm^2 = 2(w^2 + 10w)

Divide 2 on both sides. 

96cm^2 = w^2 + 10w

Subtract 96 on both sides. 

0 = w^2 + 10w - 96

Factor it out. 
0 = (w - __)(w + ___)
0 = (w - 6)(w+16)

We have two possible answers of: 
w = 6
w = -16

The only answer which makes sense is the positive one, because a box in real life can't have negative length. 
So, 
w = 6 cm.