 ## Volume of a Cylinder

The space covered by a solid cylinder is known as the volume of that cylinder.  Volume of a cylinder is given by the product of its area of circular base (πr2) and the height (h) of the cylinder.

i.e. Volume of cylinder = Area of the circular base × height
= πr2 × h
= πr2h

Volume of the cylinder = πr2h

### Volume of material of a hollow cylinder

A hollow cylinder is a solid bounded by two co-axial cylinders of the same height and different radii. For example - water pipe, rubber pipe etc.
Let R be the external radius and r be the internal radius of a hollow cylinder as given in the figure below. Then,

The volume of the material of hollow cylinder = External volume – internal volume
= πR2h – πr2h
= πh(R2 – r2)

### Workout Examples

Example 1: Find volume of the cylinder:

Solution: Here,
Diameter of the cylinder (d) = 14cm
Radius of the cylinder (r) = 14cm/2 = 7cm
Height of the cylinder (h) = 20cm

We know,
Volume of cylinder (V) = πr2h
= 22/7 × 72 × 20
= 22 × 7 × 20
= 3080cm3

Thus, the volume of cylinder is 3080cm3.

Example 2: The volume of a cylinder is 770cm3. If the height of the cylinder is 5cm, find the radius of the base of cylinder.

Solution: Here,
Height of the cylinder (h) = 5cm.
Volume of cylinder = 770cm3
i.e.      πr2h = 770
or,      22/7 × r2 × 5 = 770
or,      110/7 × r2 = 770
or,      r2 = 770 × 7/110
or,      r2 = 72
or,      r = 7cm

Thus, the radius of the base of cylinder is 7cm.

Example 3: The sum of the height and the radius of a cylinder is 37cm. If the area of total surface is 1628cm3, find the volume of the cylinder.

Solution: Here,
r + h = 37cm ……………….. (i)

Total surface area (TSA) of cylinder = 1628cm3
i.e.      2πr(r + h)  = 1628
or,      2 × 22/7 × r × 37 = 1628
or,      1628/7 × r = 1628
or,      r = 1628 × 7/1628
or,      r = 7cm

Putting the value of r in (i),
7 + h = 37
or,      h = 37 – 7
or,      h = 30cm

Now,
Volume of cylinder = πr2h
= 22/7 × 72 × 30
= 4620cm3

Thus, the volume of cylinder is 4620cm3.

Example 4: In the adjoining figure, the internal and external radii of the metallic pipe are 3cm and 4cm respectively. If the length of the pipe is 35cm, find the volume of the metal.

Solution: Here,
The internal radius of the pipe (r) = 3cm.
The external radius of the pipe (R) = 4cm
The height (or length) of the pipe (h) = 35cm

Now,
The volume of the metal = πh(R2 – r2)
= 22/7 × 35 × (42 – 32)
= 22 × 5 × (16 – 9)
= 110 × 7
= 770cm3

Thus, the volume of the metal in the pipe is 770cm3.

You can comment your questions or problems regarding the volume and surface area of cylinders here.