Question
Find the surface area of a cylinder with a base radius length of 5 ft. and a height of 8 ft. Use π=3.14 .(1 point)
ft.2
ft.2
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 of the base,
- \( h \) is the height of the cylinder.
Given:
- \( r = 5 \) ft,
- \( h = 8 \) ft,
- \( \pi = 3.14 \).
Now, let's calculate the surface area step by step.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157 \text{ ft}^2
\]
2. Calculate the area of the side (lateral surface area):
\[
2\pi rh = 2 \times 3.14 \times 5 \times 8 = 2 \times 3.14 \times 40 = 251.2 \text{ ft}^2
\]
3. Add the areas together to get the total surface area:
\[
\text{Surface Area} = 157 + 251.2 = 408.2 \text{ ft}^2
\]
Thus, the surface area of the cylinder is \( \boxed{408.2} \) ft².
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
Given:
- \( r = 5 \) ft,
- \( h = 8 \) ft,
- \( \pi = 3.14 \).
Now, let's calculate the surface area step by step.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157 \text{ ft}^2
\]
2. Calculate the area of the side (lateral surface area):
\[
2\pi rh = 2 \times 3.14 \times 5 \times 8 = 2 \times 3.14 \times 40 = 251.2 \text{ ft}^2
\]
3. Add the areas together to get the total surface area:
\[
\text{Surface Area} = 157 + 251.2 = 408.2 \text{ ft}^2
\]
Thus, the surface area of the cylinder is \( \boxed{408.2} \) ft².