A cone having fixed volume has semi-vertical angle of π 4 . At an instant when its height is decreasing at the rate of 2 m / s, its radius increases at a rate equal to

Question

A cone having fixed volume has semi-vertical angle of π 4 . At an instant when its height is decreasing at the rate of 2 m / s, its radius increases at a rate equal to, 2 m / s, 4 m / s, 1 m / s, 8 m / s

MARKS App · Accepted Answer

As, V = 1 3 π r 2 h ⇒ d V d t = π 3 r 2 d h d t + h ⋅ 2 r d r d t = 0 ⇒ r d h d t = - 2 h d r d t Also, r h = t a n π 4 ⇒ r = h ∴ d h d t = - 2 d r d t ⇒ d r d t = - 1 2 d h d t ⇒ d r d t = + 1 ⇒ radius increases at 1 m / s .

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