Q16. - Algebra 1

Question

PAINTING A cabinet is 6 feet high, 3 feet wide, and 2 feet long. The entire outside surface of the cabinet is being painted except for the bottom. What is the surface area of the cabinet that is being painted?

Step-by-Step Solution

Answer

The surface area of the cabinet that is being painted is 30 square feet.

Step 1. State the formula.

The formula for surface area of a rectangular prism is $S=lw+wh+hl$, where S is the surface area, l is the length, w is the width and h is the height of the rectangular prism.

The area of the bottom of a rectangular prism is nothing but lw.

Step 2. List the given data.

The cabinet is in the shape of a rectangular prism of length 2 ft, width 3 ft and height 6 ft. Then, $l=2\mathrm{ft}$, $w=3\mathrm{ft}$ and $h=6\mathrm{ft}$.

Step 3. Calculate the required surface area.

The entire outside surface of the cabinet is being painted except for the bottom. Then, the surface area of the cabinet that is being painted is $S-lw$.

 

Put $S=lw+wh+hl$ in $S-lw$ to get $wh+hl$.

 

Put $l=2$, $w=3$ and $h=6$ in $wh+hl$ to get,

$$\begin{gathered} wh+hl=\left(3\right)\left(6\right)+\left(6\right)\left(2\right) \\ =18+12 \\ =30 \end{gathered}$$

So, $wh+hl=30$.

Step 4. Determine the unit.

Since the unit of length, width and height are all given as feet, the unit of the surface area must be square feet.

 

So, the surface area of the cabinet that is being painted is 30 square feet.