Question

Question

A shed has the shape of a rectangular prism. The area of the floor of the shed is 63 square feet. The length of the shed is 2

feet greater than the width. The height is 1 foot less than the width.

What is the volume of the shed in cubic feet?

Answer 1

378 Cubic feet

Explanation:

Given a rectangular prism shaped shed:

Area of the floor of the shed = 63 square feet.

Let the width of the shed=w

The length of the shed is 2 feet greater than the width.

Therefore: Length =w+2

Base Area = Length X Width

So: w(w+2)=63

`w^2+2w-63=0\\w^2+9w-7w-63=0\\w(w+9)-7(w+9)=0\\(w-7)(w+9)=0\\w=7 ft, w\\eq -9`

Width =7ft

Length =9 ft

The height is 1 foot less than the width.

Height =7-1=6 ft

Volume of a rectangular prism = Base Area X Height

=63 X 6

=378 cubic feet

Therefore, the volume of the shed is 378 cubic feet.