# Area and Circumference of a Circle

Here we will discuss about the area and circumference (Perimeter) of a circle and some solved example problems.

The area (A) of a circle or circular region is given by

A = πr$$^{2}$$

where r is the radius and, by definition,

π = $$\frac{\textrm{circumference}}{\textrm{diameter}}$$ = $$\frac{22}{7}$$ (approximately).

The circumference (P) of a circle with radius r is given by, P = 2πr

or,

The perimeter (circumference) of a circular region, with radius r is given by, P = 2πr

Solved example problems on finding the area and circumference (Perimeter) of a circle:

1. The radius of a circular field is 21 m, find its perimeter and area. (Use π = $$\frac{22}{7}$$)

Solution:

According to the question, given r = 21 m.

Then, perimeter of a circular field = 2πr

= 2 × $$\frac{22}{7}$$ × 21 m

= 2 × 22 × 3 m

= 132 m

Area of a circular field = πr$$^{2}$$

= $$\frac{22}{7}$$ × 21$$^{2}$$ m$$^{2}$$

= $$\frac{22}{7}$$ × 21 × 21 m$$^{2}$$

= 22 × 3 × 21 m$$^{2}$$

= 1386 m$$^{2}$$

2. The perimeter of a circular plate is 132 cm, find its area. (Use π = $$\frac{22}{7}$$)

Solution:

Let the radius of the plate be r.

Then, perimeter of a circular plate = 2πr

or, 132 cm = 2 × $$\frac{22}{7}$$ × r

or, r = $$\frac{132 \times 7}{2 \times 22}$$ cm

= $$\frac{6 \times 7}{2}$$

= 21 cm

Therefore, area of a circular plate = πr$$^{2}$$

= $$\frac{22}{7}$$ × 21$$^{2}$$ cm$$^{2}$$

= $$\frac{22}{7}$$ × 21 × 21 cm$$^{2}$$

= 22 × 3 × 21 cm$$^{2}$$

= 1386 cm$$^{2}$$

3. If the area of a circle is 616 cm$$^{2}$$ then, find its circumference. (Use π = $$\frac{22}{7}$$)

Solution:

Let the radius of the circle be r cm.

Area of the circle = πr$$^{2}$$

or, 616 cm$$^{2}$$ = $$\frac{22}{7}$$ × r$$^{2}$$

or, r$$^{2}$$ = $$\frac{616 \times 7}{22}$$ cm$$^{2}$$

or, r = $$\sqrt{\frac{616 \times 7}{22}}$$ cm

= $$\sqrt{28 \times 7}$$ cm

= $$\sqrt{2 \times 7 \times 2 \times 7}$$ cm

= $$\sqrt{14 \times 14}$$ cm

= 14 cm

Therefore, radius of the circle = 14 cm.

Therefore, circumference of the circle = 2πr

= 2 × $$\frac{22}{7}$$ × 14

= 2 × 22 × 2 cm

= 88 cm

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