Question
A rectangular tank is 80m long and 25m broad. Water flows into it through a pipe whose cross-section is 25cm2, at the rate of 16km per hour. How much the level of the water rises in the tank in 45 minutes?
✓
Answer
Consider 'h' be the rise in water level.
Volume of water in rectangular tank = 8000 × 2500 × h cm2
Cross-sectional area of the pipe = 25cm2
Water coming out of the pipe forms a cuboid of base area 25cm2 and length equal to the distance travelled in 45 minutes with the speed 16km/hour
i.e., length = Length $=16000\times100\times\frac{45}{60}\text{cm}$
Therefore, The Volume of water coming out pipe in 45 minutes $=25\times16000\times100\times\Big(\frac{45}{60}\Big)$
Now, volume of water in the tank = Volume of water coming out of the pipe in 45 minutes
$\Rightarrow8000\times2500\times\text{h}=16000\times100\times\frac{45}{60}\times25$
$\Rightarrow\text{h}=\frac{25\times16000\times100\times45}{60\times8000\times2500}=1.5\text{cm}$
Volume of water in rectangular tank = 8000 × 2500 × h cm2
Cross-sectional area of the pipe = 25cm2
Water coming out of the pipe forms a cuboid of base area 25cm2 and length equal to the distance travelled in 45 minutes with the speed 16km/hour
i.e., length = Length $=16000\times100\times\frac{45}{60}\text{cm}$
Therefore, The Volume of water coming out pipe in 45 minutes $=25\times16000\times100\times\Big(\frac{45}{60}\Big)$
Now, volume of water in the tank = Volume of water coming out of the pipe in 45 minutes
$\Rightarrow8000\times2500\times\text{h}=16000\times100\times\frac{45}{60}\times25$
$\Rightarrow\text{h}=\frac{25\times16000\times100\times45}{60\times8000\times2500}=1.5\text{cm}$
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