Question

Find how much time, the cylindrical pond having radius 3.5m and depth 7m can be filled by a tap which gives the water at the rate of 60 litres per minute:
a.32.06 hours
b.3.06 hours
c.74.79 hours
d.12.06 hours

Answer 1

Hint: The rate of volume of water is equal to volume of water per unit time.
$\text{Rate of Volume = }\dfrac{\text{Volume}}{\text{Time}}$
Here volume is in litres and time is in minutes because rate of volume is given in litres per minute.

Complete step by step answer:
A cylindrical pond is given so we have to find the volume of the cylinder.
We know that, Volume of cylinder =$\pi {{r}^{2}}h$where r is the radius of the cylinder and h is the depth of the cylinder.
Now, radius is given as 3.5m and depth is given as 7m. Substituting these values in the volume of cylinder we get:
$\pi {{\left( 3.5 \right)}^{2}}\left( 7 \right){{m}^{3}}$
Substituting the value of$\pi =3.14$in the above solution we get,
$\begin{aligned} & 3.14{{\left( 3.5 \right)}^{3}}\left( 7 \right){{m}^{3}} \\\ & =269.255{{m}^{3}} \\\ \end{aligned}$
As the volume that we are getting is in m3 but it is given that volume is in litres so we have to convert m3 to litres. From the metric conversions we know that, $1{{m}^{3}}=1000litres$.So, we have to convert the above volume into litres by multiplying the above volume to 1000 and the converted volume equals 269.255×1000 or 269255.
Substituting the volume and time in the formula of rate of volume we get,
$\begin{aligned} & \text{Rate = }\dfrac{\text{Volume}\left( \text{litres} \right)}{\text{Time}\left( \text{minutes} \right)} \\\ & \Rightarrow 60=\dfrac{269255}{\text{Time}} \\\ & \Rightarrow \text{Time = }\dfrac{269255}{60} \\\ & \Rightarrow \text{Time = 4487}\text{.583} \\\ \end{aligned}$
So the time we are getting is in minutes but the options are in hours so we have to convert minutes into hours by dividing this time to 60.
$\begin{aligned} & \dfrac{4487.583}{60} \\\ & =74.79\text{ hours} \\\ \end{aligned}$
Hence, the correct option is (c).

Note: Be careful about the unit conversions. Like in this question, volume is given in litres but the calculated volume is in m3 so we tend to forget to convert into litres and same with the time, in options time is asked in hours but the time we get from the formula is in minutes.