To find the volume of a cylinder, use the formula:
Volume=πr2h\text{Volume}=\pi r^2hVolume=πr2h
where:
- rrr is the radius of the circular base of the cylinder,
- hhh is the height of the cylinder,
- π\pi π (pi) is approximately 3.14159.
Steps to calculate the volume:
- Measure the radius of the base of the cylinder.
- Square the radius (multiply the radius by itself).
- Multiply the squared radius by π\pi π.
- Multiply the result by the height of the cylinder.
This formula calculates the amount of space inside the cylinder, essentially the area of the circular base times the height
. For example, if a cylinder has a radius of 3 cm and a height of 5 cm, the volume is:
V=π×32×5=π×9×5=45π≈141.37 cm3V=\pi \times 3^2\times 5=\pi \times 9\times 5=45\pi \approx 141.37\text{ cm}^3V=π×32×5=π×9×5=45π≈141.37 cm3
This method applies to right circular cylinders. For hollow cylinders (cylindrical shells), the volume is calculated by subtracting the volume of the inner cylinder from the outer cylinder:
Volume=π(R2−r2)h\text{Volume}=\pi (R^2-r^2)hVolume=π(R2−r2)h
where RRR is the external radius and rrr is the internal radius
. In summary, the key formula is:
V=πr2h\boxed{V=\pi r^2h}V=πr2h
Use this to find the volume of any solid cylinder.