An equilateral triangle’s sides increase at the rate of 2 c m / s e c . If the area of its incircle increases at a rate of k c m 2 / s e c (when the length of the side is 6 π c m ), then the value of k is

Question

An equilateral triangle’s sides increase at the rate of 2 c m / s e c . If the area of its incircle increases at a rate of k c m 2 / s e c (when the length of the side is 6 π c m ), then the value of k is,

MARKS App · Accepted Answer

r a 2 = t a n 30 o 2 r a = 1 3 ⇒ r = a 2 3 ∴ Area of incircle, A = π r 2 = π a 2 12 ∴ d A d t = 2 π a 12 d a d t = π 6 ⋅ 6 π ⋅ 2 = 2 c m 2 / s e c .

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