Question

A room is in the shape of a rectangular prism with dimensions 20 feet $\times$ 12 feet $\times$ 10 feet. If the cost of the wallpaper is $\$4$ per square feet, what will the cost of decorating all the walls of the room?

• A. $\$1280$
• B. $\$2840$
• C. $\$3240$
• D. $\$2560$

Answer 1

The correct option is D $\$2560$

Given, the cost of the wallpaper is $\$4$ per sq ft.
We need to find the total cost of the wallpaper required to decorate the entire room.

Let’s find the lateral surface area.
There are 4 walls, 2 pairs of walls with the dimensions
20ft $\times$ 10 ft and 12ft $\times$ 10 ft.
So, the lateral surface area$=2\times (20\times 10)+2\times (12\times 10)$
$=2\times \left(200\right)+2\times \left(120\right)$
$=400+240=640$sq ft

Therefore, the lateral surface area = 640 sq ft.
Total cost of the wallpaper = lateral surface area $\times$ wallpaper cost per sq ft $=640\times 4=\$2560$