The radius of a circle is 5 m. Find the circumference of the circle whose area is 49 times the area of the given circle.

Given:

Radius of original circle = r = 5 m

Area of new circle = 49 times area of original circle.

Let R be the radius of new circle.

$⇒ πR^2 = 49 \times πr^2\\[1em] ⇒ \dfrac{22}{7} \times R^2 = 49 \times \dfrac{22}{7} \times 5^2\\[1em] ⇒ \cancel{\dfrac{22}{7}} \times R^2 = 49 \times \cancel{\dfrac{22}{7}} \times 5^2\\[1em] ⇒ R^2 = 49 \times 25\\[1em] ⇒ R^2 = 1,225\\[1em] ⇒ R = \sqrt{1,225}\\[1em] ⇒ R = 35 \text{ m}^2$

Circumference of new circle = 2πR

$= 2 \times \dfrac{22}{7} \times 35\\[1em] = \dfrac{44}{7} \times 35\\[1em] = \dfrac{1,540}{7}\\[1em] = 220 \text{ m}^2$

Hence, the circumference of new circle is 220 m.