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The following piece of writing presents the formula derivation of a cylinder's volume, and it's calculation.

Arjun Kulkarni
Mar 14, 2019

Volume can be simply defined as the space occupied by a 3D object. Often, we need to know how much of a solid, liquid, or gaseous matter can be placed within a container. If you want to find out how much soda can be stored in a can, you need to find out the volume of the can. Hence volume calculations are important in our day-to-day lives.

A cylinder is a 3D geometric figure. It has a rounded surface, and is bound by two circular surfaces on its top and bottom.

The formula for the area of a circle is πr2. A cylindrical surface also has a certain height.

The formula for the volume of a cylinder is: πr^{2}h,

where "r" is the radius of the two circles on each side of the cylinder, and "h" is the cylinder's height.

The formula for the volume of a cylinder is: πr

where "r" is the radius of the two circles on each side of the cylinder, and "h" is the cylinder's height.

Example: You have a cylinder whose radius is 10 in and height is 14 in. Simply substitute the values in the formula:

πr^{2}h

V= 22/7 * 10^{2} * 14

V= 4400 in^{3}.

The unit for denoting the volume is written as the cube of the measured units. Here, both measurements are in inches, the volume unit will be "in^{3} or cubic inches".

πr

V= 22/7 * 10

V= 4400 in

The unit for denoting the volume is written as the cube of the measured units. Here, both measurements are in inches, the volume unit will be "in

Now let us see how to measure volume in Gallons. One US gallon is 231 cubic inches. Hence, by dividing the result by 231, you get the volume in gallons.

4400 in^{3}/231

= 19.0476 gallons.

This means that a cylinder that has a radius of 10 inches and a height of 14 inches, will hold approximately 19 gallons of a liquid.

4400 in

= 19.0476 gallons.

This means that a cylinder that has a radius of 10 inches and a height of 14 inches, will hold approximately 19 gallons of a liquid.