# Volume and Surface Area of a Cylinder

## Cylinder

- Solids like measuring jar,
- circular pillars,
- circular pencils,
- road rollers
- and gas cylinder, etc…

These shapes are called cylindrical shape.

## Volume of a Cylinder

For a cylinder of base radius = r and height of the cylinder = h

Then we have

**V = (πr ^{2} h) cubic units**

**where,**

V = Volume of Cylinder

π (pi)= 3.14159265358979 but we generally take 3.14 (constant)

r = Radius of circular surface of Cylinder (as shown in above figure)

h = Height of Cylinder (as shown in above figure)

## Surface Area of a Cylinder

The area of the top = πr^{2}

The are of the bottom = πr^{2}

Area of the Side = 2πrh

Therefore total Surface area can be given by,

Surface Area of a Cylinder = 2πrh +2πr^{2}

**Surface Area of a Cylinder = 2πr(r+h)**

### Examples

**Question 1: Calculate the volume of a given cylinder having height 30 cm and base radius of 14 cm. (Take pi = 22/7)**

**Solution**:

Given:

Height = 30 cm

radius = 14 cm

we know that;

Volume, V = πr^{2}h cubic units

V=(22/7) × 14 × 14 × 30

V= 18480 cm^{3}

Therefore, the volume of a cylinder = 18480 cm^{3}

**Question 2: Calculate the radius of the base of a cylindrical container of volume 450 cm ^{3}. Height of the cylindrical container is 40 cm. (Take pi = 22/7)**

**Solution**:

Given:

Volume = 450 cm^{3}

Height = 35 cm

We know from the formula of cylinder;

Volume, V = πr2h cubic units

So, 450 = (22/7) × r2 × 35

r2 = (450 × 7)/(22 × 35) = 3150/770 = 4

Therefore, r = 2 cm

Therefore, the radius of a cylinder = 2 cm.