Find the radius and area of a circle, whose circumference is :

(i) 132 cm

(ii) 22 m

(i) Let r be the radius of the circle.

The circumference of a circle = 132 cm

As we know, the circumference of the circle = 2πr

$⇒ 2 \times \dfrac{22}{7} \times r = 132\\[1em] ⇒ \dfrac{44}{7} \times r = 132\\[1em] ⇒ r = \dfrac{132 \times 7}{44}\\[1em] ⇒ r = \dfrac{924}{44}\\[1em] ⇒ r = 21 \text{ cm}$

And, area of the circle = πr²

$= \dfrac{22}{7} \times 21^2\\[1em] = \dfrac{22}{7} \times 441\\[1em] = \dfrac{9,702}{7}\\[1em] = 1,386 \text{ cm}^2$

Hence, the radius of the circle is 21 cm and the area is 1,386 cm².

(ii) Let r be the radius of the circle.

The circumference of a circle = 22 cm

As we know, the circumference of the circle = 2πr

$⇒ 2 \times \dfrac{22}{7} \times r = 22\\[1em] ⇒ \dfrac{44}{7} \times r = 22\\[1em] ⇒ r = \dfrac{22 \times 7}{44}\\[1em] ⇒ r = \dfrac{154}{44}\\[1em] ⇒ r = 3.5 \text{ m}$

And, area of the circle = πr²

$= \dfrac{22}{7} \times 3.5^2\\[1em] = \dfrac{22}{7} \times 12.25\\[1em] = \dfrac{269.50}{7}\\[1em] = 38.5 \text{ m}^2$

Hence, the radius of the circle is 3.5 m and the area is 38.5 m².