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?

1 Answer
Nov 14, 2015

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