Volume of a Cone Formula

# Volume of a Cone Formula

## 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, πr2h = 3 × volume of the conical flask

Volume of the conical flask = 1/3 × πr2h

Hence, Volume of a cone = 1/3 × πr2h

### Volume of Cone Formula

Volume of a cone = 1/3 × πr2h

### 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 × πr2h

= 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 × πr2h

= 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 × πr2h

264 = 1/3 × 22/7 × r2 × 28

264 = 1/3 × 22/7 × r2 × 28

264 × 21 = 616 × r2

r2 = 5544/616

r2 = 9

r = 3 cm

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