# Cylinder volume – diameter, height in in (ft) – in

Cylinder diameter (* d*):

Cylinder height (* h*):

The volume of a cylinder * V* is:

^{3}

^{3}

^{3}

^{3}

## How to calculate the volume of a cylinder?

The volume of the cylinder is determined by the formula:

* V=h*Π*d^{2}/4*, где

* h* – cylinder height (cylinder length);

* Π = 3.1415926535 – *mathematical constant equal to the ratio of the circumference of a circle to its diameter;

* d *– cylinder base diameter.

The volume of a cylinder is equal to the area of the base (circle) times the height of the cylinder.

If the diameter and height of the cylinder are measured in in (inches), then the volume of the cylinder is:

in cubic inch (cu in):

**V**_{in3}**= ****h**_{in}***Π*d**_{in}^{2}**/4**

in cubic feet (cu ft):

**V**_{ft}_{3 }**= (h**_{in}***Π *d**_{in}^{2}/4**) / 1 728**

in cubic yard (cu yd):

**V**_{yd}_{3}**=(h**_{in}***Π*d**_{in}^{2}/4**) / 46 656**

in cubic meters (cu m):

**V**_{m3}**=(h**_{in}***Π*d**_{in}^{2}/4**) / 61 024.744**

in liters (L):

**V**_{L}**=(h**_{i}_{n}***Π*d**_{in}^{2}/4**) / 61.0247**

For example:

*What is the volume of a cylinder with a diameter of 6 ft 10 in and a height of 9 ft 8 in?*

*Solution:*

*diameter of 6 ft 10 in = 6 x 12 in + 10 in = 82 in*

*height of 9 ft 8 in = 9 x 12 in + 8 in = 116 in*

**V**_{in3}**= ****h**_{in}***Π*d**_{in}^{2}**/4 **= 116 * 3.14159 * 82^{2 }/ 4 = 612 597.48 cu in

**V**_{ft}_{3 }**= (h**_{in}***Π *d**_{in}^{2}/4**) / 1 728 **= (116 * 3.14159 * 82^{2 }/ 4) / 1 728 = 354.51 cu ft

**V**_{yd}_{3}**=(h**_{in}***Π*d**_{in}^{2}/4**) / 46 656 **= (116 * 3.14159 * 82^{2 }/ 4) / 46 656 = 13.13 cu yd

**V**_{m3}**=(h**_{in}***Π*d**_{in}^{2}/4**) / 61 024.744 **= (116 * 3.14159 * 82^{2 }/ 4) / 61 024.744 = 10.04 cu m

**V**_{L}**=(h**_{i}_{n}***Π*d**_{in}^{2}/4**) / 6 102.47 **= (116 * 3.14159 * 82^{2 }/ 4) / 61.02= 10 039 liters