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.

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