Area and Perimeter of a Circle

We will discuss the Area and Perimeter of a Circle.

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

A = πr²

where r is the radius and, by definition, π = \(\frac{\textrm{Circumference}}{Diameter}\) = \(\frac{22}{7}\) (Approximately).

The circumference (P) of a circle, or the perimeter of a circle region, with radius r is given by

P = 2πr

Solved Examples on Area and Perimeter of a Circle:

1. The radius of a circular region is 7 m. Find its perimeter and area. (Use π = \(\frac{22}{7}\))

Solution:

Here r = 7 m. Then,

Perimeter = 2πr = 2 × \(\frac{22}{7}\) × 7 m = 44 m;

Area = πr² = \(\frac{22}{7}\) × 7² m² = 154 m².

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 = 2πr

⟹ 132 cm = 2 × \(\frac{22}{7}\) × r

⟹ 132 cm = \(\frac{44}{7}\) × r

⟹ \(\frac{44}{7}\) × r = 132 cm

⟹ r = 132 × \(\frac{7}{44}\)

⟹ r = \(\frac{924}{44}\)

⟹ r = 21 cm.

Therefore, area of the plate = πr² = \(\frac{22}{7}\) × 21² cm²

                                        = \(\frac{22}{7}\) × 441 cm²

                                        = \(\frac{9702}{7}\) cm²

                                        = 1386 cm²

10th Grade Math

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