Mathematics

Find the circumference of the circle whose area is equal to the sum of the areas of three circles with radius 2 cm, 3 cm and 6 cm.

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Let the radius of resultant circle be r cm.

Given,

Area of resultant circle is equal to the sum of the areas of three circles with radius 2 cm, 3 cm and 6 cm.

⇒ πr² = π(2)² + π(3)² + π(6)²

⇒ πr² = π[(2)² + (3)² + (6)²]

⇒ r² = 2² + 3² + 6²

⇒ r² = 4 + 9 + 36

⇒ r² = 49

⇒ r = $\sqrt{49}$ = 7 cm.

Circumference of circle = 2πr

= $2 \times \dfrac{22}{7} \times 7$

= 44 cm.

Hence, circumference of circle = 44 cm.

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