Question
Find the surface area of a cylinder with a radius of 6in and a height of 10in. Leave it in terms of π .(1 point) Responses 192π in2 192π in2 192π in3 192π in3 603π in2 603π in2 192 in2
Answers
GPT-4o mini
To find the surface area of a cylinder, you can use the formula:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
For this cylinder:
- Radius \( r = 6 \) in
- Height \( h = 10 \) in
Now, we can plug in the values:
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2\pi (6)^2 = 2\pi (36) = 72\pi \text{ in}^2
\]
2. Calculate the lateral surface area:
\[
2\pi rh = 2\pi (6)(10) = 120\pi \text{ in}^2
\]
3. Now, add both areas together to get the total surface area:
\[
\text{Surface Area} = 72\pi + 120\pi = 192\pi \text{ in}^2
\]
Thus, the surface area of the cylinder is \( \boxed{192\pi} \) in².
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
For this cylinder:
- Radius \( r = 6 \) in
- Height \( h = 10 \) in
Now, we can plug in the values:
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2\pi (6)^2 = 2\pi (36) = 72\pi \text{ in}^2
\]
2. Calculate the lateral surface area:
\[
2\pi rh = 2\pi (6)(10) = 120\pi \text{ in}^2
\]
3. Now, add both areas together to get the total surface area:
\[
\text{Surface Area} = 72\pi + 120\pi = 192\pi \text{ in}^2
\]
Thus, the surface area of the cylinder is \( \boxed{192\pi} \) in².