Surface Area of Circle Formula

Introduction to Surface Area of Circle

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, etc. The area of the circle formula is useful for measuring the space occupied by a circular field or a plot. Suppose you have the plot to fence it, then the area formula will help you to check how much fencing is required. Or suppose you have to buy a table cloth, then how many portions of cloth is needed to cover it completely.

Hence, the concept of area as well as the perimeter is introduced in Maths, to figure out such scenarios. But, one common question that arises among most people is “does a circle have volume?”. The answer is “No”. Since a circle is a two-dimensional shape, it does not have volume. It has only an area and perimeter. So, we don’t have the volume of a circle. In this article, let us discuss in detail the area of a circle, surface area and its circumference with examples.

What is a Circle?

A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point. Basically, a circle is a closed curve with its outer line equidistant from the center. The fixed distance from the point is the radius of the circle. In real life, you will get many examples of the circle such as a wheel, pizzas, a circular ground, etc. Now let us learn, what are the terms used in the case of a circle.

Radius

The radius of the circle is the line that joins the center of the circle to the outer boundary. It is usually represented by ‘r’ or ‘R’. In the formula for the area and circumference of a circle, radius plays an important role which you will learn later.

Diameter

The diameter of the circle is the line that divides the circle into two equal parts. In an easy way we can say, it is just the double of the radius of the circle and is represented by ‘d’ or ‘D’. Therefore,

d = 2r or D = 2R

If the diameter of the circle is known to us, we can calculate the radius of the circle, such as;

r = d/2 or R = D/2

Circumference of Circle

A perimeter of closed figures is defined as the length of its boundary. When it comes to circles, the perimeter is given using a different name. It is called the “Circumference” of the circle. This circumference is the length of the boundary of the circle. If we open the circle to form a straight line, then the length of the straight line is the circumference. To define the circumference of the circle, knowledge of a term known as ‘pi’ is required.

Surface Area of Circle Formula

The formula for the area of a circle is:

A = πr²

where A represents the area and r is the radius of the circle. The value of π is approximately 3.14159, but you can use a more precise value depending on the level of accuracy required for your calculations.

The area of the circle formula is useful for measuring the space occupied by a circular field or a plot. Suppose you have the plot to fence it, then the area formula will help you to check how much fencing is required. Or suppose you have to buy a table cloth, then how many portions of cloth is needed to cover it completely.

Hence, the concept of area as well as the perimeter is introduced in Maths, to figure out such scenarios. But, one common question that arises among most people is “does a circle have volume?”. The answer is “No”. Since a circle is a two-dimensional shape, it does not have volume. It has only an area and perimeter. So, we don’t have the volume of a circle. In this article, let us discuss in detail the area of a circle, surface area and its circumference with examples.

Solved Examples on Area of a Circle Formula

Example 1: What is the radius of the circle whose surface area is 314.159 sq.cm?

Solution:

By the formula of the surface area of the circle, we know;

A = π x r2

Now, substituting the value:

314.159 = π x r2

314.159 = 3.14 x r2

r2 = 314.159/3.14

r2 = 100.05

r = √100.05

r = 10 cm

Example 2: Find the circumference and the area of circle if the radius is 7 cm.

Solution:

Given: Radius, r = 7 cm

We know that the circumference/ perimeter of the circle is 2πr cm.

Now, substitute the radius value, we get

C = 2×(22/7)× 7

C = 2×22

C = 44 cm

Thus, the circumference of the circle is 44 cm.

Now, the area of the circle is πr2 cm2

A = (22/7) × 7 × 7

A = 22 × 7

A = 154 cm2

Frequently Asked Questions on Area of a Circle Formula

1: What is meant by area of circle?

Answer: The area of circle is the region occupied by circle in the two-dimensional space.

2: How to calculate the area of a circle?

Answer: The area of circle can be calculated by using the formulas:

Area = π x r2, in terms of radius ‘r’.

Area = (π/4) x d2, in terms of diameter, ‘d’.

Area = C^2/4π, in terms of circumference, ‘C’.

3: What is the perimeter of circle?

Answer: The perimeter of circle is nothing but the circumference, which is equal to twice of product of pi (π) and radius of circle, i.e., 2πr.

4: What is the area of a circle with radius 3 cm, in terms of π?

Answer: Given, r = 3 cm.

We know that the area of circle is πr2 square units

Hence, A = π x 32 = 9π cm2.

5: Find the circumference of circle in terms of π, whose radius is 14 cm.

Answer: We know that the circumference of a circle is 2πr units.

Hence, C = 2π(14) = 28π cm.

6: Find the radius of the circle, if its area is 340 square centimeters.

Answer: We know that, Area of a circle = πr2 square units

Hence, 340 =3.14 r2

Hence, r2 = 340/3.14

R^2 = 108.28

Hence, r = 10.4 cm.

Hence, radius of a circle = 10.4 cm

7: Determine the area of the circle in terms of pi, if radius = 6 cm.

Answer: We know that, Area = πr2

A = π(6)2

A = 36π

Hence, the area of a circle is 36π, if the radius is 6 cm.

8: Find the area of a circle, if its circumference is 128 inches.

Answer: The area of a circle is 1303.8 square inches if its circumference is 128 inches.