In Geometry, a cone is a three-dimensional shape, which is formed by the set of line segments joining from the base to the common point, called the apex. The base of the cone is a circle, which is the flat face of a cone. In this article, we are going to discuss what is the base area of a cone, the formula and many solved examples in detail.
What is the Base Area of a Cone?
In Maths, the base area of a cone is the area or region occupied by the flat face of a cone. If we observe the flat face of the cone, we can find a circle. Thus, the base area of a cone is the area of a circle. It is generally measured in square units, such as cm2, m2, ft2, and so on.
Base Area of a Cone Formula
If “r” is the base radius of a cone, then the formula to find the base area of a cone is given by:
Base Area of a Cone = πr2 square units
Since the radius is half of the diameter, the base area of a cone in terms of diameter is given by:
Base Area of a Cone = (πD2)/4 square units
Here “D” represents the base diameter of a cone.
Examples on Base Area of a Cone
Go through the below examples to understand the base area of a cone.
Example 1:
Determine the base area of a cone whose base radius is 3 cm. (Use π= 3.14)
Solution:
Given: Base radius of a cone = 3 cm
We know that the formula for the base area of a cone is πr2 square units
Substitute r = 3 cm in the formula, we get
Base Area of a cone = 3.14×(3)2
= 3.14× 9
= 28.26 cm2
Hence, the base area of a cone whose base radius is 3 cm = 28.26 cm2.
Example 2:
Compute the base radius area of a cone whose base diameter is 4 cm. (Use π= 3.14)
Solution:
Given: Base diameter = 4 cm
Thus, base radius, r = 4/2 = 2 cm
As we know, the base area of a cone formula is πr2 square units
Base Area = 3.14 × (2)2
Base Area = 3.14 × 4 = 12.56 cm2
Therefore, the base area of the cone whose base diameter is 4 cm = 12.56 cm2.
Example 3:
Estimate the base area of a cone whose base diameter is 7 cm. (Use π= 22/7)
Solution:
Given: Base diameter = 7 cm
We know that, the base area of a cone = (πD2)/4 square units
Now substitute D = 7 cm,
πD2 = (22/7)(7)2
πD2 = 154
Thus, the base area of the cone = 154/4 = 38.5 cm2.
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Practice Questions
Solve the following problems:
- Find the base area of a cone whose base radius is 7 cm.
- Determine the base area of a cone whose base diameter is 10 cm.
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Frequently Asked Questions on Base Area of a Cone
What is the base area of a cone?
The base area of a cone is the region occupied by the flat face of a cone. In other words, the area of a cone is the area of a circle.
What is the base of a cone?
The base of a cone is a circle.
What is the formula for the base area of a cone?
If “r” is the base radius of a cone, then the base area of a cone formula is πr2 square units.
How to express the base area of a cone?
The base area of a cone is expressed in square units, such m2, cm2, etc.
How to find the base area of a cone if the base diameter is given?
If the base diameter of the cone is given, then the formula for the base area of a cone is (πD2)/4 square units.
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