A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan⁻¹(1/2). Water is poured into it at a constant rate of 5 cubic metres per hour. The rate at which the depth of water is increasing when th…

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan⁻¹(1/2). Water is poured into it at a constant rate of 5 cubic metres per hour. The rate at which the depth of water is increasing when the depth is 2 m is:

• A. 5/π m/h
• B. 1/π m/h
• C. 5/(4π) m/h
• D. 4/(5π) m/h

Answer: A) 5/π m/h

Explanation: tan θ = r/h = 1/2 → r = h/2. Volume V = (1/3)πr²h = (1/3)π(h/2)²h = (π/12)h³. dV/dt = (π/4)h² dh/dt. 5 = (π/4)(4) dh/dt → 5 = π dh/dt → dh/dt = 5/π m/h.