Question

How to calculate the volume of a cylinder and a cube

Answer 1

To calculate the volume of a cylinder and a cube, you'll use different formulas for each shape.

### Volume of a Cylinder

The formula for the volume \( V \) of a cylinder is:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14159.

### Steps:
1. Measure or obtain the radius \( r \) of the cylinder's base.
2. Measure or obtain the height \( h \) of the cylinder.
3. Plug the radius and height into the formula and calculate.

### Example:
If the radius of the base is 3 cm and the height is 5 cm, the volume is:

\[
V = \pi (3)^2 (5) = \pi \times 9 \times 5 = 45\pi \approx 141.37 \text{ cm}^3
\]

---

### Volume of a Cube

The formula for the volume \( V \) of a cube is:

\[
V = a^3
\]

where:
- \( V \) is the volume,
- \( a \) is the length of one side of the cube.

### Steps:
1. Measure or obtain the length of one side \( a \) of the cube.
2. Plug the side length into the formula and calculate.

### Example:
If the length of one side is 4 cm, the volume is:

\[
V = (4)^3 = 64 \text{ cm}^3
\]

These formulas will allow you to calculate the volumes of a cylinder and a cube accurately.