Question

Water is supplied to a city population for general use (not for drinking) from a river through a cylindrical pipe. The radius of the cross-section of the pipe is 20cm. The speed of water through the pipe is 18km/hr. Find the quantity of water in litres which is supplied to the city in two hours. (Take $\pi =3.14$ and $1{{m}^{3}}=1000litres$)
(a) 4521600 litres
(b) 4528500 litres
(c) 4571600 litres
(d) 2221600 litres

Answer 1

Hint:Here, first we have to find the area of the cross section, A by the formula, A = $\pi {{r}^{2}}$. Then find the length of the water flow in 2 hours by the formula, $Distance=Speed\times Time$. Next, find the volume of the water flow by the formula: $Volume=Area\times Length$. Here, we have to do the conversion also, that is change km into cm and then change cm into litres.

Complete step-by-step answer:
Here, we are given that water is supplied to a city population for general use from a river through a cylindrical pipe. It is also given that the radius of the cross section of the pipe is 20cm and the speed of water through the pipe is 18km/hr.
Now, we have to find the quantity of water in litres which is supplied to the city in two hours.
First, we have to find the area of the cross section.
We have radius, r = 20cm
Then, area of the cross-section of pipe, A = $\pi {{r}^{2}}$
$\begin{aligned} & \Rightarrow A=3.14\times 20\times 20 \\\ & \Rightarrow A=1256c{{m}^{2}} \\\ \end{aligned}$
Now, we have to find the length, L of the water flow in 2 hours.
We have the formula that:
$Distance=Speed\times Time$
We have the speed of the water through the pipe = 18km/hr
We also have the time = 2hr
By substituting these values in the formula,
$\begin{aligned} & \Rightarrow L=2\times 18 \\\ & \Rightarrow L=36km \\\ \end{aligned}$
We have got the unit in km, now we have to change it into cm.
We know that 1km = 100000cm
Hence, we can write:
$\begin{aligned} & L=36\times 100000 \\\ & L=3600000cm \\\ \end{aligned}$
Next, we have to find the volume of water flow, V which is supplied to the city in 2 hours.
We know that:
Volume of the water flow = area of cross section $\times$ length of water flow
$\begin{aligned} & \Rightarrow V=1256\times 3600000 \\\ & \Rightarrow V=4521600000c{{m}^{3}} \\\ \end{aligned}$
Next,we have to convert $c{{m}^{3}}$ into litres.
We know that:
$\begin{aligned} & 1000c{{m}^{3}}=1litre \\\ & \Rightarrow 1c{{m}^{3}}=\dfrac{1}{1000}litre \\\ \end{aligned}$
Therefore, we can write:
$\begin{aligned} & 4521600000c{{m}^{3}}=\dfrac{4521600000}{1000} \\\ & 4521600000c{{m}^{3}}=4521600litres \\\ \end{aligned}$
Hence, the volume of the water flow is 4521600litres.
Therefore, we can say that the quantity of water which is supplied to the city in two hours is 4521600litres.
So, the correct answer for this question is option (a).

Note: The volume of the cylinder is $\pi {{r}^{2}}h$, since the height is not given we can calculate the volume by using area where:Volume = Area of the cross section $\times$ Length.Here, the pipe is in the form of a cylinder and the cross section of the cylinder is a circle. Hence, while calculating the cross sectional area we have to take the area of the circle which is $\pi {{r}^{2}}$.Students have to take care while converting from km to cm and $cm^3$ to litres.And have to remember the formula of finding volume and distance for solving these types of questions.