Question
Anjali needs to paint the outside of an entire coffee can for an art class project.
Given the figure below, calculate the canβs surface area to help her determine how much paint she will need.
6 inches on top
6 1/4 inches on the side
Use 3.14 for pi (π).
Formula for surface area of a cylinder: SA = 2πr 2
+ 2πrβ
(1 point)
Responses
56.52 in2
56.52 in2
117.75 in2
117.75 in2
174.27 in2
174.27 in2
197,34 in2
197,34 in2
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Given the figure below, calculate the canβs surface area to help her determine how much paint she will need.
6 inches on top
6 1/4 inches on the side
Use 3.14 for pi (π).
Formula for surface area of a cylinder: SA = 2πr 2
+ 2πrβ
(1 point)
Responses
56.52 in2
56.52 in2
117.75 in2
117.75 in2
174.27 in2
174.27 in2
197,34 in2
197,34 in2
Skip to navigation
Answers
GPT-4o mini
To calculate the surface area of the coffee can, we 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 top of the can, and
- \(h\) is the height of the can.
From the problem, the diameter of the top of the can is given as 6 inches. Therefore, we can calculate the radius \(r\) as:
\[
r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches}
\]
The height \(h\) of the can is given as 6 1/4 inches, which can be expressed as:
\[
h = 6.25 \text{ inches}
\]
Now we can substitute the values of \(r\) and \(h\) 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 \(2\pi rh\):
\[
2\pi rh = 2 \times 3.14 \times 3 \times 6.25
\]
\[
= 2 \times 3.14 \times 18.75 = 2 \times 58.875 = 117.75 \text{ in}^2
\]
3. Now, add both areas together:
\[
SA = 56.52 + 117.75 = 174.27 \text{ in}^2
\]
Thus, the total surface area of the coffee can is:
\[
\boxed{174.27 \text{ in}^2}
\]
\[
SA = 2\pi r^2 + 2\pi rh
\]
where:
- \(r\) is the radius of the top of the can, and
- \(h\) is the height of the can.
From the problem, the diameter of the top of the can is given as 6 inches. Therefore, we can calculate the radius \(r\) as:
\[
r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches}
\]
The height \(h\) of the can is given as 6 1/4 inches, which can be expressed as:
\[
h = 6.25 \text{ inches}
\]
Now we can substitute the values of \(r\) and \(h\) 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 \(2\pi rh\):
\[
2\pi rh = 2 \times 3.14 \times 3 \times 6.25
\]
\[
= 2 \times 3.14 \times 18.75 = 2 \times 58.875 = 117.75 \text{ in}^2
\]
3. Now, add both areas together:
\[
SA = 56.52 + 117.75 = 174.27 \text{ in}^2
\]
Thus, the total surface area of the coffee can is:
\[
\boxed{174.27 \text{ in}^2}
\]