Volume of a Cone Formula
The volume of a cone is the amount of space it occupies, which depends on the size of its circular base and its height. There are various ways to calculate the volume of a cone depending on the known measurements, such as radius and height, diameter and height, or slant height and radius. Below are all the formulas for calculating the volume of a cone, with detailed explanations and examples for each method.
Formulas for the Volume of a Cone
Using Radius and Height:
If the radius
The volume
Using Diameter and Height:
If the diameter
The volume
Using Slant Height and Radius:
If the slant height
The volume
In these formulas:
is the radius of the base of the cone is the diameter of the base of the cone, where is the slant height of the cone is the vertical height of the cone, where (Pi) is approximately equal to 3.14159
Detailed Explanation of Each Formula
1 Formula for Volume Using Radius and Height
The formula
Example 1: Calculating Volume with Radius and Height
Problem: Find the volume of a cone with a radius of
Solution:
- Write down the formula:
. - Substitute
and : . - Calculate
: . - Multiply:
(using ).
The volume of the cone is approximately
2 Formula for Volume Using Diameter and Height
The formula
Example 2: Calculating Volume with Diameter and Height
Problem: A cone has a diameter of
Solution:
- Write down the formula:
. - Substitute
and : . - Calculate
: . - Multiply:
.
The volume of the cone is approximately
3 Formula for Volume Using Slant Height and Radius
The formula
Example 3: Calculating Volume with Slant Height and Radius
Problem: A cone has a radius of
Solution:
- Write down the formula:
. - Substitute
and : . - Calculate
and : . - Simplify inside the square root:
. - Find
: .
The volume of the cone is approximately
These examples demonstrate how to calculate the volume of a cone using different known measurements, whether it’s the radius and height, diameter and height, or slant height and radius.