Question

Water is pouring into a cuboidal reservoir at the rate of $60$ liters per minute. If the volume of the reservoir is $108{\mathrm{m}}^3$, find the number of hours it will take to fill the reservoir.

Answer 1

Given that the reservoir is cuboidal in shape.

$$\begin{gathered} \mathrm{The}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{reservoir}=108{\mathrm{m}}^3 \\ \Rightarrow =108\times 1000\mathrm{litres}\left[\because 1{\mathrm{m}}^3=1000\mathrm{litres}\right] \\ \Rightarrow =108000\mathrm{litres} \end{gathered}$$

The volume of water flowing into the reservoir in one minute is $60$ liters

The volume of water pouring into the reservoir in $1$ hour is computed as,

$$\begin{gathered} =60\times 60 \\ =3600\mathrm{litres}\mathrm{per}\mathrm{hour} \end{gathered}$$

The required number of hours to fill the reservoir is computed as,

$$\begin{gathered} \therefore \mathrm{Time}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{reservoir}}{\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{one}\mathrm{hour}} \\ \Rightarrow =\frac{108000}{3600} \\ \Rightarrow =30\mathrm{hours} \end{gathered}$$

Hence, the number of hours it will take to fill the reservoir is $30$ hours.