Question

A room is in the shape of a rectangular prism with dimensions 20 ft $\times$ 12 ft $\times$ 10 ft. Cost to decorate entire room @ $\$4/{\text{ft}}^2$ is

• A. $2560
• B. $2660
• C. $2860

Answer 1

The correct option is A $2560

In the rectangular prism shaped room,



$\text{Wallpaper cost}=\$4/{\text{ft}}^2$

Total cost for the wallpaper to decorate entire room is required.
Lateral surface area has to be found out

There are 4 walls and 2 pairs
So, $\text{Lateral surface area}$
$=2\left[\right(l\times h)+(w\times h\left)\right]$
$=2\left[\right(l\times h)+(w\times h\left)\right]$
$=2\left[\right(20\times 10)+(12\times 10\left)\right]$
$=2(200+120){\text{ft}}^2$
$=2\left(320\right){\text{ft}}^2$
$=640{\text{ft}}^2$

$\therefore \text{Lateral Surface Area}=640{\text{ft}}^2$

$\text{Wallpaper cost}=\$4/{\text{ft}}^2$
$\text{Lateral Surface Area}=640{\text{ft}}^2$
$\therefore \text{Total cost for wallpaper}=\text{Lateral Surface area}\times \text{Wallpaper cost}=640{\text{ft}}^2\times 4/{\text{ft}}^2=\$2560$