Question
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Part 1
Find the volume of the cylinder.
9 m
9 m
Question content area bottom
Part 1
The volume of the cylinder in terms of pi is
182.25 pi cubic m.
(Use integers or decimals for any numbers in the expression. Type an exact answer in terms of pi.)
Part 2
The volume of the cylinder to the nearest tenth is
enter your response here cubic m.
(Type an integer or decimal rounded to the nearest tenth as needed.)
The volume of the cylinder in terms of iscubic m.(Use integers or decimals for any numbers in the expression. Type an exact answer in terms of .)The volume of the cylinder to the nearest tenth iscubic m.(Type an integer or decimal rounded to the nearest tenth as needed.)
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Part 1
Find the volume of the cylinder.
9 m
9 m
Question content area bottom
Part 1
The volume of the cylinder in terms of pi is
182.25 pi cubic m.
(Use integers or decimals for any numbers in the expression. Type an exact answer in terms of pi.)
Part 2
The volume of the cylinder to the nearest tenth is
enter your response here cubic m.
(Type an integer or decimal rounded to the nearest tenth as needed.)
The volume of the cylinder in terms of iscubic m.(Use integers or decimals for any numbers in the expression. Type an exact answer in terms of .)The volume of the cylinder to the nearest tenth iscubic m.(Type an integer or decimal rounded to the nearest tenth as needed.)
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Answers
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 of the base of the cylinder, and
- \( h \) is the height of the cylinder.
From the information provided:
- The height \( h = 9 \, m \)
- The diameter is also given to be \( 9 \, m \), which means the radius \( r = \frac{9}{2} = 4.5 \, m \).
Now, you can substitute the values into the volume formula:
\[
V = \pi (4.5)^2 (9)
\]
Calculating \( (4.5)^2 \):
\[
(4.5)^2 = 20.25
\]
Now substitute that back into the volume formula:
\[
V = \pi (20.25)(9) = 182.25\pi \, \text{cubic meters}
\]
### Part 1: Volume of the Cylinder in Terms of Pi
The volume of the cylinder in terms of pi is:
\[
182.25\pi \, \text{cubic m}
\]
### Part 2: Volume of the Cylinder to the Nearest Tenth
Now you need to calculate the numerical value of the volume.
To find the volume numerically without pi:
\[
V = 182.25\pi \approx 182.25 \times 3.14159 \approx 572.557
\]
Rounding to the nearest tenth gives you:
\[
572.6 \, \text{cubic m}
\]
### Summary
- Volume of the cylinder in terms of pi: **182.25π cubic m**
- Volume of the cylinder to the nearest tenth: **572.6 cubic m**
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cylinder, and
- \( h \) is the height of the cylinder.
From the information provided:
- The height \( h = 9 \, m \)
- The diameter is also given to be \( 9 \, m \), which means the radius \( r = \frac{9}{2} = 4.5 \, m \).
Now, you can substitute the values into the volume formula:
\[
V = \pi (4.5)^2 (9)
\]
Calculating \( (4.5)^2 \):
\[
(4.5)^2 = 20.25
\]
Now substitute that back into the volume formula:
\[
V = \pi (20.25)(9) = 182.25\pi \, \text{cubic meters}
\]
### Part 1: Volume of the Cylinder in Terms of Pi
The volume of the cylinder in terms of pi is:
\[
182.25\pi \, \text{cubic m}
\]
### Part 2: Volume of the Cylinder to the Nearest Tenth
Now you need to calculate the numerical value of the volume.
To find the volume numerically without pi:
\[
V = 182.25\pi \approx 182.25 \times 3.14159 \approx 572.557
\]
Rounding to the nearest tenth gives you:
\[
572.6 \, \text{cubic m}
\]
### Summary
- Volume of the cylinder in terms of pi: **182.25π cubic m**
- Volume of the cylinder to the nearest tenth: **572.6 cubic m**