# A rectangular tank is 80 m long and 25 m broad.

Question:

A rectangular tank is $80 \mathrm{~m}$ long and $25 \mathrm{~m}$ broad. Water flows into it through a pipe whose cross-section is $25 \mathrm{~cm}^{2}$, at the rate of $16 \mathrm{~km}$ per hour. How much the level of the water rises in the tank in 45 minutes?

Solution:

Consider 'h' be the rise in water level.

Volume of water in rectangular tank $=8000 * 2500 * \mathrm{~h} \mathrm{~cm}^{2}$

Cross-sectional area of the pipe $=25 \mathrm{~cm}^{2}$

Water coming out of the pipe forms a cuboid of base area $25 \mathrm{~cm}^{2}$ and length equal to the distance travelled in 45

minutes with the speed 16 km/hour

i.e., length = Length = 16000 ∗ 100 ∗ 45/60 cm

Therefore, The Volume of water coming out pipe in 45 minutes = 25 * 16000 * 100 * (45/60)

Now, volume of water in the tank = Volume of water coming out of the pipe in 45 minutes

⇒ 8000 ∗ 2500 ∗ h = 16000 ∗ 100 ∗ 45/60 ∗ 25

$\Rightarrow \mathrm{h}=\frac{25 * 16000 * 100 * 45}{60 * 8000 * 2500}=1.5 \mathrm{~cm}$