College

What is the volume of a cylinder with a diameter of 10 cm and a height of 5 cm?

A. 1570.8 cm³
B. 196.3 cm³
C. 98.2 cm³
D. 392.7 cm³

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.