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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 = πr2

where r is the radius and, by definition,

π = circumferencediameter = 227 (approximately).

Area and Circumference of a Circle

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 = 227)

Solution:

According to the question, given r = 21 m.

Then, perimeter of a circular field = 2πr

                                                 = 2 × 227 × 21 m

                                                 = 2 × 22 × 3 m

                                                 = 132 m

Area of a circular field = πr2

                                 = 227 × 212 m2

                                 = 227 × 21 × 21 m2

                                 = 22 × 3 × 21 m2

                                 = 1386 m2


2. The perimeter of a circular plate is 132 cm, find its area. (Use π = 227)

Solution:

Let the radius of the plate be r.

Then, perimeter of a circular plate = 2πr

or, 132 cm = 2 × 227 × r

or, r = 132×72×22 cm

       = 6×72

       = 21 cm

Therefore, area of a circular plate = πr2

                                                  = 227 × 212 cm2

                                                  = 227 × 21 × 21 cm2

                                                  = 22 × 3 × 21 cm2

                                                  = 1386 cm2


3. If the area of a circle is 616 cm2 then, find its circumference. (Use π = 227)

Solution:

Let the radius of the circle be r cm.

Area of the circle = πr2

or, 616 cm2 = 227 × r2

or, r2 = 616×722 cm2

 or, r = 616×722 cm

        = 28×7 cm

        = 2×7×2×7 cm

        = 14×14 cm

        = 14 cm

Therefore, radius of the circle = 14 cm.

Therefore, circumference of the circle = 2πr

                                                       = 2 × 227 × 14

                                                       = 2 × 22 × 2 cm

                                                       = 88 cm





9th Grade Math

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