Base Area of a Cone

The base area of a cone is defined as the area of the flat surface (bottom surface) of the cone. A cone is a 3-D object which tapers smoothly from a flat base (usually circular) to a point called the apex. In other words, it is a shape formed by a set of line segments, coming from the base, connecting to a common point. These lines start from the points in the base and end at the apex. In this lesson, we will discuss more about the base area of a cone.

The base of the cone is a flat face which is a circle hence the base area of a cone is nothing but the area of this circle. A cone is a three-dimensional shape. The surface area of a cone is the space occupied by the curved surface and the base surface of the cone.

For a given cone, with the known base radius, base area (or flat surface area) is π times square of the radius and can also be represented as, A = πr² where r is the base radius. The base area of the cone can also be given in terms of the diameter of the cone which gives the formula, A = π(D/2)² = (πD²)/4 where D is the diameter of the base.

The base area of the cone can be given by the formula π r². Thus, we follow the steps shown below to find the base area of a cone.

• Step 1: Identify the base radius of the cone and name this radius as r.
• Step 2: If the radius is given, find the base area of a cone using the following base area of a cone formula A = πr². Else if the diameter is given, find the base area of a cone using the following base area of a cone formula = (π/4) D². Use π = 22/7 or 3.14
• Step 3: Represent the final answer in square units.

Example: What is the base area of a cone having base radius = 4 units? (Use π = 3.14)

Solution: Given that r = 4 units
Thus, base area of the cone = π × r² = 3.14 × 4² = 50.24 units²

Answer: Base area of the cone = 50.24 units²

What Is the Base Area of a Cone?

The base of the cone is the quantity that shows the area covered by the circular base of the cone. A cone is a 3-D object which tapers smoothly from a flat base (usually circular) to a point called the apex. In other words, it is a shape formed by a set of line segments, coming from the base, connecting to a common point. These lines start from the points in the base and end at the apex.

What Is the Formula for Base Area of a Cone?

The formula for the base area of a cone is A = πr², where r is the radius of the base of the cone. The formula for the base area of the cone can also be shown in terms of the diameter of a cone as A = π(D/2)² = (πD²)/4, where D is the diameter of the base.

How to Find the Base Area of a Cone?

We can find the base area of a cone using the following steps

• Step 1: Identify the base radius of the cone.
• Step 2: Find the base area of a cone using the following base area of a cone formula A = πr².
• Step 3: Write the obtained answer in square units.

How to Find the Base Area of a Cone With Diameter?

We can find the base area of a cone with diameter using the following steps

• Step 1: Identify the base diameter of the cone.
• Step 2: Find the base area of a cone using the following base area of a cone formula A = (π/4) D².
• Step 3: Write the answer so obtained in square units.

How Do You Find the Base Area of Cone With Slant Height?

We can find the base area of a cone with slant height using the following steps

• Step 1: Identify the base radius and slant height of the cone.
• Step 2: Use the Pythagoras Theorem to obtain the relation L = √(r² + h²) where r is the base radius, L is the slant height and h is the height of the cone.
• Step 2: Once the required values are obtained, find the base area of a cone using the formula A = πr².
• Step 3: Write the answer in square units.

How to Find the Radius of Cone If Base Area of a Cone is Given?

We can find the radius of the cone if the base area of a cone is given using the following steps

• Step 1: Identify the given dimensions of the cone and assume the radius of the cone as "r"
• Step 2: Substitute the given values in the formula A = πr².
• Step 3: Solve for "r".
• Step 4: Write the obtained answer in units.

What Happens to the Base Area of a Cone If the Radius of Base is Doubled?

The base area of the cone quadruples if the radius of the base is doubled as "r" in the formula gets substituted by "2r" using the formula, A = πr² = π(2r)² = 4(πr²) which is four times the original value of the base area of cone.