Q17. - Algebra 1

Question

SOUP A soup can is 4 inches tall and has a diameter of $3\frac{1}{4}$  inches. How much paper is needed for the label on the can? Round your answer to the nearest tenth.

Step-by-Step Solution

Answer

The amount of paper needed for the label on the can is 40.9 square inches.

Step 1. State the formula.

The formula for curved surface area of a cylinder is  $S=2\pi rh$, where S is the surface area, r is the radius and h is the height of the cylinder.

 

The formula for radius of a cylinder is $r=\frac{d}{2}$, where d is the diameter of the cylinder.

Step 2. List the given data.

The soup can which is in the form of a cylinder has diameter $3\frac{1}{4}\mathrm{in}.$ and height 4 in. Then, $d=3\frac{1}{4}\mathrm{in}.$ and $h=4\mathrm{in}.$

Step 3. Calculate the radius.

Put $d=3\frac{1}{4}$ in $r=\frac{d}{2}$ to get,

$$\begin{gathered} r=\frac{3\frac{1}{4}}{2} \\ =\frac{\frac{13}{4}}{2} \\ =\frac{13}{8} \end{gathered}$$

So, $r=\frac{13}{8}$.

Step 4. Calculate the required surface area.

A label of a soup can is put on its curved surface, that is, excluding its top and bottom.

Then, the amount of paper needed is equal to the curved surface area of the can.

 

Put $r=\frac{13}{8}$, $h=4$ and $\pi =\frac{22}{7}$ in $S=2\pi rh$ to get,

$$\begin{gathered} S=2\left(\frac{22}{7}\right)\left(\frac{13}{8}\right)4 \\ =2\left(\frac{22}{7}\right)\left(\frac{13}{2}\right) \\ =\left(\frac{22}{7}\right)13 \\ \approx 40.9\left(\mathrm{roundedtothenearesttenth}\right) \end{gathered}$$

So, $S\approx 40.9$.

Step 4. Determine the unit.

Since the unit of radius and height are both given as inches, the unit of the surface area must be square inches.

 

So, the curved surface area of the soup can, rounded to the nearest tenth, is 40.9 square inches.

 

Thus, the amount of paper needed for the label on the can is also 40.9 square inches.