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.
Mensuration
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Answer
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 = = 7 cm.
Circumference of circle = 2πr
=
= 44 cm.
Hence, circumference of circle = 44 cm.
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