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

(i) 154 cm²

(ii) 6.16 m²

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

The area of circle = 154 cm²

As we know, the area of the circle = πr²

$⇒ \dfrac{22}{7} \times r^2 = 154\\[1em] ⇒ r^2 = \dfrac{154 \times 7}{22}\\[1em] ⇒ r^2 = \dfrac{1,078}{22}\\[1em] ⇒ r^2 = 49\\[1em] ⇒ r = \sqrt{49}\\[1em] ⇒ r = 7 \text{ cm}$

Circumference of the circle = 2πr

$= 2 \times \dfrac{22}{7} \times 7\\[1em] = \dfrac{44}{7} \times 7\\[1em] = \dfrac{308}{7}\\[1em] = 44 \text{ cm}$

Hence, the radius of the circle is 7 cm and the circumference is 44 cm.

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

The area of circle = 6.16 m²

As we know, the area of the circle = πr²

$⇒ \dfrac{22}{7} \times r^2 = 6.16\\[1em] ⇒ r^2 = \dfrac{6.16 \times 7}{22}\\[1em] ⇒ r^2 = \dfrac{43.12}{22}\\[1em] ⇒ r^2 = 1.96\\[1em] ⇒ r = \sqrt{1.96}\\[1em] ⇒ r = 1.4 \text{ m}$

Circumference of the circle = 2πr

$= 2 \times \dfrac{22}{7} \times 1.4\\[1em] = \dfrac{44}{7} \times 1.4\\[1em] = \dfrac{61.6}{7}\\[1em] = 8.8 \text{ m}$

Hence, the radius of the circle is 1.4 m and the circumference is 8.8 m.