A hemispherical tank is full of water. It is connected to a pipe that empties it at a rate of 7 litres per second. How much appro…

Question

A hemispherical tank is full of water. It is connected to a pipe that empties it at a rate of 7 litres per second. How much approximate time (in minutes) will it take to empty half the tank if the internal radius of the tank is 2.1 meters? (Use π = 22/7 and 1 m³ = 1000 liters)

1. A. 23 minutes (Correct answer)
2. B. 16 minutes
3. C. 46 minutes
4. D. 11 minutes

Correct Answer

Option A — 23 minutes

Detailed Solution & Explanation

The correct answer is 23 minutes.

Key Points

• Volume of a hemisphere = (2/3)πr³, with r = 2.1 m:
  • r³ = 2.1³ = 9.261
  • V = (2/3) × (22/7) × 9.261 = 19.404 m³
• Half the tank is 19.404 / 2 = 9.702 m³, and 1 m³ = 1000 litres, so that is 9,702 litres.
• At 7 litres per second: 9,702 / 7 = 1,386 seconds = 1386/60 = 23.1 ≈ 23 minutes.

Additional Information

• Keep the sphere family distinct: sphere = (4/3)πr³, hemisphere = (2/3)πr³, and a hemisphere's curved surface = 2πr² with total surface = 3πr² once the flat circular face is included.
• A radius of 2.1 (a multiple of 0.7) is chosen so that π = 22/7 cancels cleanly — treat such values as a signal to use the fraction rather than 3.14.
• Watch the units at every step: metres cubed to litres, then seconds to minutes. Most errors in this question type are unit slips rather than formula errors.
• Note that "half the tank" halves the volume, not the radius — halving the radius would cut the volume to one-eighth.