The volume of a cylinder has been explained in this article along with solved examples for better understanding. The example questions from the calculation of the volume of a cylinder will help the students to develop problem-solving abilities. Apart from the volume of cylinder definition, the derivation and applications are also discussed.

## About a Cylinder and its Volume

Cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another. Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cylindrical box. In other words, we mean to calculate the capacity of this box. The capacity of a cylindrical box is basically equal to the volume of the cylinder involved. Thus, the volume of a three-dimensional shape, in general, is equal to the amount of space occupied by that shape.

The general formula for the calculation of the volume of a cylinder is derived below. As a cylinder can be seen as a collection of multiple congruent disks stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height. Volume of a cylinder of base radius ‘r’, and height ‘h’ = (area of base) × h = πr^{2}h

## Volume of a Cylinder Derivation

For any cylinder, the volume will be base times the height. Now, if the base circle has a radius “r”, the volume will be-

\(Volume\; of\;a\,Cylinder\;=\;base\, \times\, height\)

\(=>Volume\;=\;\pi\,\times\,r^{2}\,\times\,h\)

## Problems Related to the Calculation of a Volume of a Cylinder:

**Question 1:** **Calculate the volume of a cylinder having height 20 cm and base radius of 14 cm. (Take pi = 22/7)**

* Solution: *Volume of a cylinder = πr

^{2}h \(\large \Rightarrow\) \(\frac{ 22}{7}\times 14 \times 14\times 20\) = 12320 cm

^{3}

*Question 2:* Calculate the radius of base of a cylindrical container of volume 440 cm^{3}. Height of the cylindrical container is 35 cm. (Take pi = 22/7)

* Solution: *Volume of a cylinder = (area of base) × height of cylinder Area of base = (Volume of cylinder)/ (height of cylinder) = 440/35cm

^{2}\(\large \Rightarrow\) \(\frac{ 22}{7}\times r^2 \)= 440/35 \(\large \Rightarrow\) r

^{2}= 4 \(\large \Rightarrow\) r = 2 cm

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