Question
A cylinder is shown below.
Which diagram is a net for the cylinder?
What is the surface area of the cylinder?
Use 𝜋≈3.14 and write your answer as a decimal rounded to the nearest tenth.
about
square inches
Which diagram is a net for the cylinder?
What is the surface area of the cylinder?
Use 𝜋≈3.14 and write your answer as a decimal rounded to the nearest tenth.
about
square inches
Answers
GPT-4o mini
To determine the net of a cylinder, it includes two circles (the top and bottom faces of the cylinder) and a rectangle (the side of the cylinder) that wraps around the circles.
### Surface Area of a Cylinder
The surface area \( A \) of a cylinder can be calculated using the formula:
\[
A = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
### Calculation Steps
1. **Find the area of the circles**: \( 2\pi r^2 \)
2. **Find the area of the rectangle**: \( 2\pi rh \)
3. **Add both areas together**.
### Example Calculation
Assuming you have the values for \( r \) and \( h \):
- If \( r = 3 \) inches and \( h = 5 \) inches:
- Area of the circles:
\( 2\pi r^2 = 2\pi(3^2) = 2\pi(9) = 18\pi \).
Using \( \pi \approx 3.14\), this gives:
\( 18 \times 3.14 \approx 56.52 \) square inches.
- Area of the rectangle:
\( 2\pi rh = 2\pi(3)(5) = 30\pi \).
Again using \( \pi \approx 3.14\):
\( 30 \times 3.14 \approx 94.2 \) square inches.
- Total Surface Area:
\[
A \approx 56.52 + 94.2 \approx 150.72 \, \text{square inches}.
\]
Rounding to the nearest tenth:
\[
A \approx 150.7 \, \text{square inches}.
\]
### Conclusion
For the exact values of \( r \) and \( h \) you have, substitute them into the formulas to compute the surface area, rounding the final result to the nearest tenth. If you have specific dimensions, please provide them for detailed calculations.
### Surface Area of a Cylinder
The surface area \( A \) of a cylinder can be calculated using the formula:
\[
A = 2\pi r^2 + 2\pi rh
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
### Calculation Steps
1. **Find the area of the circles**: \( 2\pi r^2 \)
2. **Find the area of the rectangle**: \( 2\pi rh \)
3. **Add both areas together**.
### Example Calculation
Assuming you have the values for \( r \) and \( h \):
- If \( r = 3 \) inches and \( h = 5 \) inches:
- Area of the circles:
\( 2\pi r^2 = 2\pi(3^2) = 2\pi(9) = 18\pi \).
Using \( \pi \approx 3.14\), this gives:
\( 18 \times 3.14 \approx 56.52 \) square inches.
- Area of the rectangle:
\( 2\pi rh = 2\pi(3)(5) = 30\pi \).
Again using \( \pi \approx 3.14\):
\( 30 \times 3.14 \approx 94.2 \) square inches.
- Total Surface Area:
\[
A \approx 56.52 + 94.2 \approx 150.72 \, \text{square inches}.
\]
Rounding to the nearest tenth:
\[
A \approx 150.7 \, \text{square inches}.
\]
### Conclusion
For the exact values of \( r \) and \( h \) you have, substitute them into the formulas to compute the surface area, rounding the final result to the nearest tenth. If you have specific dimensions, please provide them for detailed calculations.