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 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, volume of a three dimensional shape in general is equal to the amount of space occupied by that shape. General formula for the calculation of 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, volume of 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 = ?r^{2}h

## Problems related to the calculation of volume of a cylinder:

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

* Solution: *Volume of a cylinder = ?r

^{2}h

\(\large \Rightarrow\) \(\frac{ 22}{7}\times 14 \times 14\times 20\) = 12320 cm^{3}

*Questions:* Calculate the radius of base of a cylindrical container of volume 440 cm^{3}. Height of the cylindrical container is 35 cm. (Take ? = 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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