Area of Circles: Worked Examples

In the previous posts, we have solved problems on how to calculate the area of square and rectangle. We continue this series by solving problems involving area of circles.

The formula for the area of a circle is

A = pi r2

Where A is the Area, r is the radius, and pi is the irrational number which is approximately equal to 3.1416. In solving area of circles, the approximate value of pi is usually given.

Problem 1

Find the area of a circle whose radius is 12 cm. Use pi = 3.14.


Substituting to the values we have

A = pi r2
A = (3.14)(122)
A = (3.14)(144)
A = 452.16.

So, the area of the circle is equal to 452.16

Problem 2

The area of a circular garden is 50.24 sq. m. Find its diameter. Use pi = 3.14.


In this problem, area is given. We are looking for the diameter which is twice the radius.

Substituting the values to the formula, we have

A = \pi r2

50.24 = (3.14) ( r2)

Dividing both sides by 3.14, we have
(50.24)/(3.14)= (3.14)( r2)/(3.14)

16 = r2

Getting the square root of both sides, we have

4 = r

Therefore, the radius of the circle is 4cm. Since the diameter of a circle is twice its radius, the answer is (4 cm)(2) = 8 cm.

Problem 3

The diameter of a circle is 15 cm. Find its area. Use pi = 3.14 and round to the nearest tenths.


We are given the diameter, but we need the radius which is half the diameter. Therefore, the radius is 7.5 cm.

Substituting to the formula, we have

A = pi r2
A = (3.14)(7.52)
A = (3.14)(56.25)
A = 176.625

Rounding to the nearest tenths, we have 176.6.

Therefore, the area of the circle is equal to 176.6 sq. cm.

How to Calculate the Area of a Circle

Last week, we have discussed how to calculate the circumference of a circle. In this post, we learn how to calculate the area of a circle. The area of a circle which we will denote by A is equal to the product of \pi and the square of its radius r. Putting it in equation, we have

A = \pi r^2.

In the examinations, the value of \pi is specified. They usually use 3.14, 3.1416 or \frac{22}{7}.

If you can recall, the radius is the segment from the center to the point on the circle as shown below. The radius is half the diameter. The diameter is the longest segment that you can draw from one point on the circle to another. It always passes through the center.

Note: We also use the term radius to refer to the length of the radius and diameter as the length of the diameter.   » Read more

Introduction to the Basic Concepts of Circles

The Civil Service Exams also contain geometry problems, and so far, our discussions are mostly algebra problems. In this new series of posts, we will discuss how to solve geometry and measurement problems particularly about circles. However, before we start solving problems, let us first discuss the basic terminologies about circles.

A circle is a set of points equidistant to a point called the center of the circle. As I go around to give trainings and lectures , I usually hear the wrong definition below. I am not sure where this definition originated, but this is wrong.  » Read more

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