Question
Find the volume of a cylinder with a height of 12 inches and a diameter of 8 inches. Use 3.14 for pi.(1 point) Responses 602.88 cubic inches 602.88 cubic inches 2,411.52 cubic inches 2,411.52 cubic inches 150.72 cubic inches 150.72 cubic inches 1,808.64 cubic inches
Answers
Answer
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Answered by
GPT-4o mini
To find the volume of a cylinder, you can use the formula:
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Find the radius**: The diameter is given as 8 inches, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ inches}
\]
2. **Use the height**: The height \( h \) is given as 12 inches.
3. **Substitute into the volume formula**:
\[
V = 3.14 \times (4)^2 \times 12
\]
4. **Calculate \( (4)^2 \)**:
\[
(4)^2 = 16
\]
5. **Now substitute this value into the volume formula**:
\[
V = 3.14 \times 16 \times 12
\]
6. **Calculate \( 16 \times 12 \)**:
\[
16 \times 12 = 192
\]
7. **Now multiply by \( 3.14 \)**:
\[
V = 3.14 \times 192
\]
8. **Calculate \( 3.14 \times 192 \)**:
\[
V = 602.88
\]
Thus, the volume of the cylinder is \( 602.88 \) cubic inches.
The correct response is **602.88 cubic inches**.
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Find the radius**: The diameter is given as 8 inches, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ inches}
\]
2. **Use the height**: The height \( h \) is given as 12 inches.
3. **Substitute into the volume formula**:
\[
V = 3.14 \times (4)^2 \times 12
\]
4. **Calculate \( (4)^2 \)**:
\[
(4)^2 = 16
\]
5. **Now substitute this value into the volume formula**:
\[
V = 3.14 \times 16 \times 12
\]
6. **Calculate \( 16 \times 12 \)**:
\[
16 \times 12 = 192
\]
7. **Now multiply by \( 3.14 \)**:
\[
V = 3.14 \times 192
\]
8. **Calculate \( 3.14 \times 192 \)**:
\[
V = 602.88
\]
Thus, the volume of the cylinder is \( 602.88 \) cubic inches.
The correct response is **602.88 cubic inches**.
Answered by
GPT-4o mini
Yes, I can confirm the calculation. Let's go through it step by step again:
1. **Radius Calculation**:
- Given diameter = 8 inches.
- Radius \( r = \frac{diameter}{2} = \frac{8}{2} = 4 \) inches.
2. **Height**:
- Given height \( h = 12 \) inches.
3. **Volume Formula**:
- The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
- Using \( \pi \approx 3.14 \):
4. **Substituting Values**:
- \( V = 3.14 \times (4)^2 \times 12 \)
5. **Calculating \( r^2 \)**:
- \( (4)^2 = 16 \)
6. **Calculating the Volume**:
\[
V = 3.14 \times 16 \times 12
\]
7. **Calculating \( 16 \times 12 \)**:
\[
16 \times 12 = 192
\]
8. **Now, multiply by \( 3.14 \)**:
\[
V = 3.14 \times 192
\]
9. **Final Calculation**:
\[
V = 602.88 \text{ cubic inches}
\]
So, the calculation is verified, and the volume of the cylinder is indeed **602.88 cubic inches**. If there’s anything else you’d like to clarify or check, feel free to ask!
1. **Radius Calculation**:
- Given diameter = 8 inches.
- Radius \( r = \frac{diameter}{2} = \frac{8}{2} = 4 \) inches.
2. **Height**:
- Given height \( h = 12 \) inches.
3. **Volume Formula**:
- The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
- Using \( \pi \approx 3.14 \):
4. **Substituting Values**:
- \( V = 3.14 \times (4)^2 \times 12 \)
5. **Calculating \( r^2 \)**:
- \( (4)^2 = 16 \)
6. **Calculating the Volume**:
\[
V = 3.14 \times 16 \times 12
\]
7. **Calculating \( 16 \times 12 \)**:
\[
16 \times 12 = 192
\]
8. **Now, multiply by \( 3.14 \)**:
\[
V = 3.14 \times 192
\]
9. **Final Calculation**:
\[
V = 602.88 \text{ cubic inches}
\]
So, the calculation is verified, and the volume of the cylinder is indeed **602.88 cubic inches**. If there’s anything else you’d like to clarify or check, feel free to ask!
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