Volume of Cone Formula: Definition, Derivation & Examples

Volume of cone formula: The volume of a cone is the amount of space it takes up. It is one of the most important geometrical figures in three dimensions. The base of a cone is circular, and it tapers down smoothly to a point known as the apex or vertex. A cone is made up of a series of line segments that link to a common point, as we all know. The line segments in a cone do not cross the circular base. The right circular cone and the oblique cone are the two forms of cones.

Cones can be found in our everyday lives in the form of ice cream cones, party hats, funnels, and other items. Students are taught the notion of a cone from an early stage in order to answer a variety of math problems. Continue reading to learn about the concept, formula, and examples that have been solved.

Volume of Cone: Definition

The volume of a cone is determined by the amount of space occupied by the cone. As you know, it is a three-dimensional structure formed by a set of line segments or lines that narrows down to a point known as the apex or vertex. The distance from the point to the base is called the height of the cone.

Let us check the types and properties of cones for a better understanding of the concept.

There are two types of cones, namely, right circular cone and oblique cone.

Right Circular Cone: It has a circular base and the axis from the vertex of the cone passes through the centre of the base. It forms a right angle perpendicular to the base.

Oblique Cone: The axis from the vertex does not directly pass through the centre of the base. The cone is not perpendicular to the base. Hence, it is called an oblique cone. It looks like a slanted or tilted cone.

Some of the properties of the cone are as follows:

The cone has a circular base with no edges.
It has a vertex or apex.
The volume of cone formula in terms of pi is ⅓ πr²h.
The total surface area of the cone is πr(l + r).
The slant height of the cone is √(r²+h²).

Check – Volume of Hemisphere

What Is the Volume of Cone Formula?

The volume of cone is calculated based on the radius of its circular base, r and height from the apex to the base, h. Please find the volume of cone formula explained below:

Volume of cone = 1/3 x Area of Base x Height of the Cone

Volume (V) = ⅓ πr²h cubic units

Where V is the volume, r is the radius, and h is the height.

Solved Examples on the Volume of Cone Formula

Check out some of the solved examples on the volume of cone formula example below:

Example 1: Find the volume of cone, if the radius is 6 cm and the height is 8 cm.

Solution: Given, r= 6 cm and h= 8 cm

V = ⅓ πr²h

V = (⅓) × (3.14) × 6² × 8

V = 301.44 cubic cm

Example 2: Find the volume of cone, if the radius is 12 cm and the height is 15 cm.

Solution: Given, r= 12 cm and h= 15 cm

V = ⅓ π Given, height (h) of cone = 15 cm Let the radius of the cone be r. Volume of cone = 1570 cm3 ⇒ 1 3 πr2h = 1570 cm3 ⇒ �1 3 × 3.14 × r2 × 15� cm = 1570 cm3 ⇒ r2 = 100 cm2 ⇒ r = 10 cm Hence, the diameter of the base of cone is 10 × 2 = 20 cm h

V = (⅓) × (3.14) × 12² × 15

V = 2260.8 cubic cm

FAQs on the Volume of Cone Formula

Some of the FAQs on the volume of cone formula are given below:

Q1. What are the types of cones?
Ans. The two types of cones are the right circular cone and oblique cone.

Q2. What are some real-life examples of cones?
Ans. Some real-life examples of cones are ice cream cones, party hats, funnels, etc.

Q3. What is the volume of cone formula?
Ans. The volume of a cone is equal to one-third of the area of the base multiplied by its height, i.e., Volume (V) = ⅓ πr²h cubic units

Q4. What is volume of cone?
Ans. The volume of cone is the amount of space occupied by the cone.

Q5. What is the volume of cone formula in terms of pi?
Ans. The volume of cone formula in terms of pi is ⅓ πr²h.

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Now you have been provided with detailed information on the volume of cone formula. Students preparing for exams can go through this article. Also, check CBSE NCERT solutions for Class 9 Maths Chapter 13 (Surface Areas and Volumes) PDF for better understanding. Take mock tests at Embibe for effective preparation.

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