Answer :
To find the volume of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] is approximately 3.14159,
- [tex]\( r \)[/tex] is the radius of the base of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder.
Here’s how we can solve the problem step-by-step:
1. Identify the given values:
- Diameter of the cylinder is 10 cm.
- Height of the cylinder is 5 cm.
2. Calculate the radius:
- The radius [tex]\( r \)[/tex] is half the diameter.
- So, [tex]\( r = \frac{10}{2} = 5 \)[/tex] cm.
3. Plug the radius and height into the volume formula:
- Substitute [tex]\( r = 5 \)[/tex] cm and [tex]\( h = 5 \)[/tex] cm into the volume formula.
- [tex]\( V = \pi \times (5)^2 \times 5 \)[/tex]
4. Calculate the volume:
- First, calculate the square of the radius: [tex]\( (5)^2 = 25 \)[/tex].
- Then multiply by the height: [tex]\( 25 \times 5 = 125 \)[/tex].
- Finally, multiply by [tex]\( \pi \)[/tex]: [tex]\( \pi \times 125 \approx 392.7 \, \text{cm}^3 \)[/tex].
Therefore, the volume of the cylinder is approximately 392.7 cm³. The answer is 392.7 cm³.
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] is approximately 3.14159,
- [tex]\( r \)[/tex] is the radius of the base of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder.
Here’s how we can solve the problem step-by-step:
1. Identify the given values:
- Diameter of the cylinder is 10 cm.
- Height of the cylinder is 5 cm.
2. Calculate the radius:
- The radius [tex]\( r \)[/tex] is half the diameter.
- So, [tex]\( r = \frac{10}{2} = 5 \)[/tex] cm.
3. Plug the radius and height into the volume formula:
- Substitute [tex]\( r = 5 \)[/tex] cm and [tex]\( h = 5 \)[/tex] cm into the volume formula.
- [tex]\( V = \pi \times (5)^2 \times 5 \)[/tex]
4. Calculate the volume:
- First, calculate the square of the radius: [tex]\( (5)^2 = 25 \)[/tex].
- Then multiply by the height: [tex]\( 25 \times 5 = 125 \)[/tex].
- Finally, multiply by [tex]\( \pi \)[/tex]: [tex]\( \pi \times 125 \approx 392.7 \, \text{cm}^3 \)[/tex].
Therefore, the volume of the cylinder is approximately 392.7 cm³. The answer is 392.7 cm³.
