Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Given: Rate of water flow$=15\ km/h$, diameter of the pipe$=14\ cm$, length of the cuboid$=50\ m$ and width of the cuboid$=44\ m$, rise of water level in the pond.

To do: To find the time to rise the water level 21 cm.

Solution:

Let the level of water in the pond rises by 21 cm in /hours.

Speed of water$=\ 15\ km/hr\ $

Diameter of pipe $=14\ cm=\frac{14}{100} \ m$

Radius of the pipe,$\ r\ =\ \frac{1}{2} \times \frac{14}{100} =\frac{7}{100} \ m$

Volume of water flowing out of the pipe in 1 hour

$=πr^{2} h=\frac{22}{7} \times \left(\frac{7}{100}\right)^{2} \times 15000$

$=\ 231\ m^{3}$

Volume of water flowing out of the pipe in t hours $=\ 231\times t\ \ m^{3}$

Volume of water in the cuboidal pond

$=\ 50\times 44\times \frac{21}{100} \ m^{3} =462\ m^{3}$

Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond

$231\times \ t\ =\ 462$

$\Rightarrow t=\frac{462}{231} =2\ hour$

$\therefore$ In 2 hours the water level in the pond will rise by 21 cm.

Related Articles Water is flowing at the rate of $15\ km/h$ through a pipe of diameter of $14\ cm$ into a cuboidal pond which is $50\ m$ long ang $44\ m$ wide. In what time will the level of water in the pond rise by $22\ cm$?
Water flows at the rate of \( 15 \mathrm{~km} / \mathrm{hr} \) through a pipe of diameter \( 14 \mathrm{~cm} \) into a cuboidal pond which is \( 50 \mathrm{~m} \) long and \( 44 \mathrm{~m} \) wide. In what time will the level of water in the pond rise by \( 21 \mathrm{~cm} \)?
Water is flowing through a cylinderical pipe, of internal diameter 2 cm, into a cylinderical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.
Water in a rectangular reservoir having base $80\ m$ by $60\ m$ is $6.5\ m$ deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side $20\ cm$, if the water runs through the pipe at the rate of $15\ km/hr$.
Water is flowing at the rate of \( 2.52 \mathrm{~km} / \mathrm{h} \) through a cylindrical pipe into a cylindrical tank, the radius of the base is \( 40 \mathrm{~cm} \). If the increase in the level of water in the tank, in half an hour is \( 3.15 \mathrm{~m} \), find the internal diameter of the pipe.
A river $3\ m$ deep and $40\ m$ wide is flowing at the rate of $2\ km$ per hour. How much water will fall into the sea in a minute?
A rectangular tank is $80\ m$ long and $25\ m$ broad. Water-flows into it through a pipe whose cross-section is $25\ cm^2$, at the rate of $16\ km$ per hour. How much the level of the water rises in the tank in $45$ minutes.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep? if the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?
A cylindrical water tank of diameter $1.4\ m$ and height $2.1\ m$ is being fed by a pipe of diameter $3.5\ cm$ through which water flows at the rate of $2$ metre per second. In how much time the tank will be filled?
A river 3 m deep and \( 40 \mathrm{~m} \) wide is flowing at the rate of \( 2 \mathrm{~km} \) per hour. How much water will fall into the sea in a minute?
A river \( 3 \mathrm{~m} \) deep and \( 40 \mathrm{~m} \) wide is flowing at the rate of \( 2 \mathrm{~km} \) per hour. How much water will fall into the sea in a minute?
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his Held, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Water flows out through a circular pipe whose internal diameter is $2\ cm$, at the rate of $6$ metres per second into a cylindrical tank. The radius of whose base is $60\ cm$. Find the rise in the level of water in $30$ minutes?
A farmer runs a pipe of internal diameter \( 20 \mathrm{~cm} \) from the canal into a cylindrical tank in his field which is \( 10 \mathrm{~m} \) in diameter and \( 2 \mathrm{~m} \) deep. If water flows through the pipe at the rate of \( 3 \mathrm{~km} / \mathrm{h} \), in how much time will the tank be filled?
A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Kickstart Your Career
Get certified by completing the course

Get Started