# Cone Formula Volume

A cone is a three-dimensional figure with one circular base and a vertex.

The volume of a cone is the amount of space it occupies or we can say that the volume denotes the capacity of the cone.

The volume of a cone is measured in cubic units (in^{3}, ft^{3}, cm^{3}, m^{3}, etc.).

## What is Cone Formula Volume?

Cone Formula Volume of a given value can be expressed as,

V=1/3(Area of the base × height of the cone), or

V=1/3πr^{2}h

Note: The formula V=1/3πr^{2}h is the same for all types of cone weather for an oblique cone or for a right cone.

Let us have a look at a few solved examples to understand the cone formula volume better.

## Solved Examples Using Cone Formula Volume

### Example 1:

### Jack is filling a conical bag with gems and wants to measure the capacity of each bag. The dimensions of the bag are such that the radius is 3 inches and the height is 8 inches. Find the volume of the conical bag.

**Solution:**

To find: Volume of the conical bag

The given dimensions are:

Radius = 3 inch, and height = 8 inch

Using Cone Formula Volume,

The volume of a cone (V)=1/3πr^{2}h

Substituting the values The volume of a cone=1/3×π×3^{2}×8

= 24π in^{3}

### Answer: The volume of the conical bag is = 24π in^{3}.

### Example 2:

### Jill went to a circus. On his way back home, a clown gifted him a conical cap. He measured the dimensions of a cap and observed that the height was 13 inches and the radius was 18 inches. Find the volume of the cap.

**Solution: **

To find: The volume of the cap

Given dimensions are:

Radius = 18 inch

Height = 13 inch

Using Cone Formula Volume,

The volume of a cone (V)=1/3πr^{2}h

Substituting the values The volume of a cone=1/3×π×18^{2}×13

= 1404π in^{3}

### Answer: The volume of the cap is 1404π in^{3}.

- Live one on one classroom and doubt clearing
- Practice worksheets in and after class for conceptual clarity
- Personalized curriculum to keep up with school