Q18. - Algebra 1

Question

CRAFTS For a craft project, Sarah is covering all the sides of a box with stickers. The length of the box is 8 inches, the width is 6 inches, and the height is 4 inches. If each sticker has a length of 2 inches and a width of 4 inches, how many stickers does she need to cover the box?

Step-by-Step Solution

Answer

Sarah needs 7 stickers to cover the box.

Step 1. State the formula.

The formula for the 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 formula for the area of a rectangle is $A=lw$, where A is the area, l is the length and w is the width of the rectangle.

Step 2. List the given data.

The box is in the form of a rectangular prism of length 8 in., width 6 in., and height 4 in. The stickers are in the form of rectangles of length 2 in. and width 4 in.

Then, for the box, $l=8\mathrm{in}.$, $h=4$, $S=lw+wh+hl$ and for the stickers, $l=2\mathrm{in}.$, $w=4\mathrm{in}.$  

Step 3. Calculate the areas.

Put $l=8$, $w=6$ and $h=4$ in $S=lw+wh+hl$ to get,

$$\begin{gathered} S=\left(8\right)\left(6\right)+\left(6\right)\left(4\right)+\left(4\right)\left(8\right) \\ =48+24+32 \\ =104 \end{gathered}$$

So, $S=104$.

Put $l=2$ and $w=4$ in $A=lw$ to get,

$$\begin{gathered} A=\left(2\right)\left(8\right) \\ =16 \end{gathered}$$

So, $A=16$.

Step 4. Determine the units.

Since the unit of length, width and height of the box are all given as inches, the unit of its surface area must be square inches. Similarly, since the unit of length and width of the stickers are both given in inches, the unit of its area must be square inches.

 

So, the surface area of the box is 104 square inches and the area of each sticker is 16 square inches.

Step 5. Determine the number of stickers.

Since the unit of both the box and each sticker is the same, the number of stickers needed to cover the box is $\frac{\mathrm{Area} \mathrm{of} \mathrm{the} \mathrm{box}}{\mathrm{Area} \mathrm{of} \mathrm{a} \mathrm{sticker}}$.

Now,

$$\begin{gathered} \frac{\mathrm{Areaofthebox}}{\mathrm{Areaofasticker}}=\frac{104}{16} \\ =6.5 \\ \approx 7\left(\mathrm{roundedtonearestunit}\right) \end{gathered}$$

This implies that 7 stickers are needed to cover the box.