Question

Anjali needs to paint the outside of an entire coffee can for an art class project.

Given the figure below, calculate the can’s surface area to help her determine how much paint she will need.

Use 3.14 for pi (𝜋).
the top and bottom of the object is 6in and the sides for it are 6 1/4in


Formula for surface area of a cylinder: SA = 2𝜋r 2
+ 2𝜋rℎ

(1 point)
Responses

56.52 in2
56.52 in2

117.75 in2
117.75 in2

174.27 in2
174.27 in2

197,34 in2

Answer 1

To calculate the surface area of the coffee can (which is a cylinder), we will use the formula for the surface area of a cylinder:

\[
SA = 2\pi r^2 + 2\pi rh
\]

where:
- \( r \) is the radius of the base, and
- \( h \) is the height of the cylinder.

Given:
- The diameter of the top and bottom of the coffee can is 6 inches. Therefore, the radius \( r \) is half of the diameter:
\[
r = \frac{6}{2} = 3 \text{ inches}
\]
- The height \( h \) of the can is 6 1/4 inches:
\[
h = 6.25 \text{ inches}
\]

Now plug in the values into the surface area formula:

1. Calculate \( 2\pi r^2 \):
\[
2\pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 \text{ in}^2
\]

2. Calculate \( 2\pi rh \):
\[
2\pi rh = 2 \times 3.14 \times 3 \times 6.25 = 2 \times 3.14 \times 18.75 = 117.75 \text{ in}^2
\]

3. Now add both parts to find the total surface area:
\[
SA = 56.52 + 117.75 = 174.27 \text{ in}^2
\]

Thus, Anjali will need a total surface area of:

\[
\boxed{174.27 \text{ in}^2}
\]

So the correct response is **174.27 in²**.