We will discuss the Area and Perimeter of a Circle.
The area (A) of a circle (or circular region) is given by
A = πr^{2}
where r is the radius and, by definition, π = \(\frac{\textrm{Circumference}}{Diameter}\) = \(\frac{22}{7}\) (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 = πr^{2} = \(\frac{22}{7}\) × 7^{2} m^{2} = 154 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 = 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 = πr^{2} = \(\frac{22}{7}\) × 21^{2 }cm^{2}
= \(\frac{22}{7}\) × 441 cm^{2}
= \(\frac{9702}{7}\) cm^{2}
= 1386 cm^{2}
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