Question

The water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a cuboidal p*** which is 550 m long and 44 m wide in what time will the level in the water in the pond ride by 21 cm

Answer 1

Error:

→ There is a mistake , it will be 50 m long , instead of 550m long .

Question:

→ Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal which is 50m long and 44m wide. In what time will the level of water in pond raise by 21cm.

Answer:

→ Time = 2 hours .

Step-by-step explanation:

Suppose, the level of water in the pond rises by 21 cm in 'x' hours.

→ Speed of water flowing through a pipe = 15 km/hr .

→ Diameter of the pipe = 14/100 m  .

Then, Radius of the pipe (r) = 7/100 m  .

∵ Volume of water flowing out of the pipe in 1 hour

= πr²h  .

= (22/7) x (7/100) x (7/100) x 15000  .

= 231 m³ .

→   Volume of water flowing out of the pipe in 'x' hours = 231x m³.

∵ Volume of water in the cuboidal pond  = lbh .

= 50 x 44 x (21/100)  .

= 462 m³ .

∵ Volume of water flowing out of the pipe in 'x' hours  = Volume of water in the cuboidal pond  raised by 21 cm .

∵  231x  = 462 .

⇒ x = 462/231 .

∴ x = 2  .

Therefore, the required time is 2 hours.

Hence, it is solved .

THANKS

Answer 2

Que :- The water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a cuboidal p*** which is 550 m long and 44 m wide in what time will the level in the water in the pond ride by 21 cm.

Solution:-


Diameter = 14 cm. = 14/100 m

=> Radius = 7/100 m

Speed of water = 15 km/hr.

Since, Pipe is in the form of Cylinder.

=> Volume of Cylinder = Volume of Water flowing through pipe in 1 hour.

$= > \pi \times {r}^{2} \times h \\ \\ = > \frac{22}{7} \times \frac{7}{100} \times \frac{7}{100} \times 15000 \\ \\ = > 22 \times 7 \times 1.5 \\ \\ = > 231 {m}^{3}$

Now, Volume of Cuboidal tank = l × b × h

=> 50 × 44 × 21/100

=> 5 × 44 × 2.1

=> 462 m^3

Volume of water flowing in x hours. = Volume of water in cuboidal tank raised by 21cm.

=> 231 × x = 462

=> x = 462/231

=> x = 2 hours.