Question
Find the surface area of a cylinder with a radius of 5 inches and a height of 10 inches. Use the approximation 3.14 for pi.
1. 471 square inches
2. 471 inches
3. 314 square inches
4. 345.4 square inches
1. 471 square inches
2. 471 inches
3. 314 square inches
4. 345.4 square inches
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.
Given:
- Radius \( r = 5 \) inches
- Height \( h = 10 \) inches
- Approximation \( \pi \approx 3.14 \)
Now, we can calculate the surface area.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157 \text{ square inches}
\]
2. Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 5 \times 10 = 2 \times 3.14 \times 50 = 314 \text{ square inches}
\]
3. Add the two areas together:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh = 157 + 314 = 471 \text{ square inches}
\]
Thus, the surface area of the cylinder is \( \boxed{471} \) square inches. The correct answer from the options provided is option 1: **471 square inches**.
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Radius \( r = 5 \) inches
- Height \( h = 10 \) inches
- Approximation \( \pi \approx 3.14 \)
Now, we can calculate the surface area.
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157 \text{ square inches}
\]
2. Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 5 \times 10 = 2 \times 3.14 \times 50 = 314 \text{ square inches}
\]
3. Add the two areas together:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh = 157 + 314 = 471 \text{ square inches}
\]
Thus, the surface area of the cylinder is \( \boxed{471} \) square inches. The correct answer from the options provided is option 1: **471 square inches**.