A roof measuring 13 meters in length and 11 meters in width had its drainage pipe closed during rainfall. After the rain, it was found that water had accumulated to a depth of 7 centimeters on the roof. The pipe through which the water drains has a diameter of 7 centimeters and discharges water in the form of a cylindrical stream at a rate of 200 meters in length per minute. Determine how long it will take for all the water to drain out once the pipe is opened.

Q.A roof measuring 13 meters in length and 11 meters in width had its drainage pipe closed during rainfall. After the rain, it was found that water had accumulated to a depth of 7 centimeters on the roof. The pipe through which the water drains has a diameter of 7 centimeters and discharges water in the form of a cylindrical stream at a rate of 200 meters in length per minute. Determine how long it will take for all the water to drain out once the pipe is opened.

Amount of water accumulated on the roof: = \(13 \times 11 \times \frac{7}{100}\) cubic meters Radius of the drainage pipe = \(\frac{7}{2}\) cm = \(\frac{7}{200}\) meters Let the time taken to drain all the water be \(x\) minutes. \[ \therefore \pi \left(\frac{7}{200}\right)^2 \times 200 \times x = 13 \times 11 \times \frac{7}{100} \] \[ \Rightarrow \frac{22 \times 49 \times x}{40000} = \frac{13 \times 11 \times 7}{100} \] \[ \Rightarrow x = \frac{13 \times 11 \times 7 \times 200}{100 \times 22 \times 7} = 13 \] \(\therefore\) It will take 13 minutes to drain all the water from the roof.