**Volume of a Cone**

A cone is a three-dimensional (3D)
figure. It has one curved face and one flat face. It has one vertex and curved
edge. A joker cap, an ice cream cone, pylon, etc. are the examples of the cone.
Its base is a circle.

The space occupied by the cone is
called its volume. The unit of
volume of a cone is cubic unit. It means the unit of volume of a cone is cu m,
cu cm, cu km, cu mm, etc.

We can find the formula to calculate
the volume of a cone by using the formula of the volume of a cylinder.

**Derivation of
Volume of Cone Formula**

To find the volume of a cone, let us
perform an activity.

**Activity: **Take an empty cylindrical flask. Take three
conical flasks full of water with the same radius and the same height as
cylinder. Now, pour the water of the three conical flasks into the empty
cylindrical flask one by one.

You will observe that the cylindrical flask will be full of water up to its brim.

It means that the capacity of a
cylindrical flask is equal to the capacity of three conical flasks.

If the base radius of the cylindrical
flask and conical flasks is r and their height is h, then the volume of
cylindrical flask = 3 × volume of the conical flask

Thus, πr^{2}h = 3 × volume of
the conical flask

Volume of the conical flask = 1/3 × πr^{2}h

Hence, **Volume of a cone =
1/3 × πr ^{2}h**

**Volume of Cone
Formula **

**Volume
of a cone = 1/3 × πr ^{2}h**

**Volume of Cone Examples
**

**Example 1:** Find the capacity of an ice cream cone whose
base radius is 10.5 cm and height is 20 cm.

**Solution: **Given: Radius of base (r) = 10.5 m and height
(h) = 20 cm

Capacity of ice cream cone = Volume of
a cone

= 1/3 × πr^{2}h

=
1/3 × 22/7 × 10.5 × 10.5 × 20

= 2310 cu cm

**Example 2:** If the base diameter of a conical flask is 28
cm and its height is 24 cm, find the volume of the liquid it can hold.

**Solution: **Given: Diameter of base (d) = 28 cm; Radius = 28/2
= 14 cm; Height = 24 cm

Volume of a cone = 1/3 × πr^{2}h

= 1/3 × 22/7 ×
14 × 14 × 24

= 4928 cu cm

**Example 3:** Find
the radius of a cone whose volume and height are 264 cu cm and 28 cm,
respectively.

**Solution: **Given: Volume of the cone = 264 cu cm, height
of the cone = 28 cm

Volume of a cone = 1/3 × πr^{2}h

264 = 1/3 × 22/7 ×
r^{2} × 28

264 = 1/3 × 22/7 ×
r^{2} × 28

264 × 21 = 616 × r^{2}

r^{2} = 5544/616

r^{2} =
9

r = 3 cm