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Answer :
To find the volume of a cylinder, you need to know the formula and how to apply it correctly.
### Formula for the Volume of a Cylinder:
The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
- [tex]\( r \)[/tex] is the radius of the base.
- [tex]\( h \)[/tex] is the height of the cylinder.
### Steps to Find the Volume:
1. Find the Radius:
- You're given the diameter of the base, which is 20 centimeters.
- The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{20}{2} = 10 \text{ centimeters}
\][/tex]
2. Calculate the Volume:
- Insert the radius and height into the formula.
- Given [tex]\( h = 8 \)[/tex] centimeters, the formula with your values becomes:
[tex]\[
V = \pi \times (10)^2 \times 8
\][/tex]
- Calculate [tex]\( (10)^2 = 100 \)[/tex].
- Now, plug into the formula:
[tex]\[
V = 3.14159 \times 100 \times 8
\][/tex]
3. Compute and Round the Volume:
- When you calculate [tex]\( 3.14159 \times 100 \times 8 \)[/tex], you get approximately 2513.2741228718346 cubic centimeters.
- Round this number to the nearest tenth to get:
[tex]\[
V \approx 2513.3 \text{ cubic centimeters}
\][/tex]
Therefore, the volume of the cylinder is approximately 2513.3 cubic centimeters.
### Formula for the Volume of a Cylinder:
The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
- [tex]\( r \)[/tex] is the radius of the base.
- [tex]\( h \)[/tex] is the height of the cylinder.
### Steps to Find the Volume:
1. Find the Radius:
- You're given the diameter of the base, which is 20 centimeters.
- The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{20}{2} = 10 \text{ centimeters}
\][/tex]
2. Calculate the Volume:
- Insert the radius and height into the formula.
- Given [tex]\( h = 8 \)[/tex] centimeters, the formula with your values becomes:
[tex]\[
V = \pi \times (10)^2 \times 8
\][/tex]
- Calculate [tex]\( (10)^2 = 100 \)[/tex].
- Now, plug into the formula:
[tex]\[
V = 3.14159 \times 100 \times 8
\][/tex]
3. Compute and Round the Volume:
- When you calculate [tex]\( 3.14159 \times 100 \times 8 \)[/tex], you get approximately 2513.2741228718346 cubic centimeters.
- Round this number to the nearest tenth to get:
[tex]\[
V \approx 2513.3 \text{ cubic centimeters}
\][/tex]
Therefore, the volume of the cylinder is approximately 2513.3 cubic centimeters.
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