# 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 r^{2}

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.

*Solution*

Substituting to the values we have

A = pi r^{2}

A = (3.14)(12^{2})

A = (3.14)(144)

A = 452.16.

So, the area of the circle is equal to 452.16 sq.cm.

**Problem 2**

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

*Solution *

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 r^{2}

50.24 = (3.14) ( r^{2})

Dividing both sides by 3.14, we have

(50.24)/(3.14)= (3.14)( r^{2})/(3.14)

16 = r^{2}

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.

*Solution*

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 r^{2}

A = (3.14)(7.5^{2})

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.