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?

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:

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