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

Answer:

#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#