trying to find the volume

Question

the area of the top of a rectangular box is 324in. squared, the area of the front of the box is 135 in. squared, and the area of the end is 60 in. squared. What is the volume of the box?

Answer 1

Start by assigning variables:

 

l = length

w = width

h = height

 

So according to the areas you've given:

 

lw = 324

lh = 135

wh = 60

 

There are 3 equations and 3 unknowns, so this should be solvable.

 

Let's try to eliminate variables 1 by 1:

 

We know that lh = 135, so

h = 135 / l

 

And we know that wh = 60. But since h = 135 / l, you can also say

w (135 / l) = 60

135 w/l = 60

w/l = 60/135 = 4/9

w = (4/9) l = 4l / 9

 

And finally, we know that lw = 324. So that means that

l(4l/9) = 324

(4/9) l² = 324

l² = 324 / (4/9) = 324 * 9 / 4 = 729

 

So l = 27

 

Since lw = 324, w = 324/27 = 12

 

And since wh = 60, h = 5.

 

So...

 

l = 27

w = 12

h = 5

 

The volume is lwh, which is 1620