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

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

Use 3.14 for pi (๐œ‹).
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 = 2๐œ‹r 2
+ 2๐œ‹rโ„Ž

(1 point)
Responses

56.52 in2
56.52 in2

117.75 in2
117.75 in2

174.27 in2
174.27 in2

197,34 in2

1 answer

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 inยฒ.