Question

A water tank is in the form of a right circular cone with radius 3 m and height 14 m. The tank is filled with water at the rate of one cubic metre per second. Find the time taken, in minutes, to fill the tank.

• A. 2.2
• B. 6.4
• C. 1.5
• D. 13.2

Answer 1

Answer:

A. 2.2

Here's how to solve this problem:

1. Calculate the Volume of the Cone:

• The formula for the volume of a cone is V = (1/3)πr²h, where:

  • V is the volume

  • r is the radius

  • h is the height

• Given:

  • r = 3 m

  • h = 14 m

• V = (1/3)π(3 m)²(14 m)

• V = (1/3)π(9 m²)(14 m)

• V = (1/3)π(126 m³)

• V = 42π m³

2. Calculate the Time to Fill the Tank (in seconds):

• The tank is filled at a rate of 1 cubic meter per second.

• Time (in seconds) = Volume / Rate

• Time = 42π m³ / 1 m³/second

• Time = 42π seconds

3. Convert Time to Minutes:

• There are 60 seconds in a minute.

• Time (in minutes) = Time (in seconds) / 60

• Time = 42π seconds / 60 seconds/minute

• Time = (42π / 60) minutes

• Time = (7π / 10) minutes

4. Approximate the Answer:

• Using π ≈ 3.14159:

  • Time ≈ (7 * 3.14159) / 10 minutes

  • Time ≈ 21.99113 / 10 minutes

  • Time ≈ 2.199113 minutes

• Rounding to two decimal places, Time ≈ 2.20 minutes

Therefore, the time taken to fill the tank is approximately 2.20 minutes.