Question

A rectangular box has two sides whose lengths are 3 centimeters and 9 centimeters and a volume of 135 `cm^3`. What is the area of its largest side?

Answer 1

`45cm^2`

Explanation:

Use the formula `V = abc`, where V stands for volume and abc stands for different sides.

Let's define our variables:
`V = 135 cm^3`
`a = 3cm`
`b = 9cm`

We want to know how long `c` is. Therefore, we can rewrite our original formula, by dividing both sides by `ab`:

`V = abc to V/(ab) = (cancel(a)cancel(b)c)/(cancel(a)cancel(b)) to V/(ab) = c`

Let's fill in the formula:

`c=(135cm^3)/(3cm*9cm)`

`c=(135cm)^cancel(3)/(27cm^cancel(2)`

`c=135/27 cm = 5cm`

To now find the biggest side, we have to multiply `b` with `c` (since they are the biggest sides):

`b * c = 9cm * 5cm = 45cm^2`