Water flows through a cylindrical pipe of diameter 5 mm at a speed of 10 m per minute. How long will it take to fill a conical vessel of base diameter 40 cm and depth 24 cm?

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Introduction / Context:Time = (volume to fill) / (flow rate). Compute the cone volume and the pipe’s volumetric flow rate from its cross-sectional area and linear speed. Given Data / Assumptions: Pipe diameter = 5 mm ⇒ radius = 2.5 mm = 0.0025 m. Flow speed = 10 m/min. Cone: base diameter 40 cm ⇒ radius 0.20 m; height 0.24 m. Concept / Approach:Flow rate Q = area * speed = πr^2 * v. Cone volume V = (1/3)πR^2h. Time t = V / Q. Step-by-Step Solution: Q = π * (0.0025)^2 * 10 = 6.25×10^-5 π m^3/minV = (1/3)π * (0.20)^2 * 0.24 = 0.0032 π m^3t = V/Q = (0.0032 π) / (6.25×10^-5 π) = 51.2 min = 51 min 12 s Verification / Alternative check:π cancels; ensure consistent SI units (metres). 0.2^2 = 0.04; 0.04*0.24/3 = 0.0032. Why Other Options Are Wrong:Small deviations come from rounding or mm–cm–m conversion errors. Common Pitfalls:Using radius as 5 mm (not diameter); forgetting 1/3 in cone volume; mixing cm and m. Final Answer:51 min 12 s

Water flows through a cylindrical pipe of diameter 5 mm at a speed of 10 m per minute. How long will it take to fill a conical vessel of base diameter 40 cm and depth 24 cm?

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