Question

water flows at the rate of 5m per minute through a cylindrical pipe whose diameter is 7cm. how long it will take to fill the conical vessel having base diameter 21m and depth 12m

Answer 1

Time required to fill the vessel is 1200 hours.

Step-by-step explanation:

The area of the cylindrical pipe with a diameter of 7 cm will be $\pi (\frac{7}{2}) ^{2} = 38.5$ cm² = 0.00385 sq. meters.

If the water is flowing at the rate of 5 m per minute, then the volume of water flowing per minute is (0.00385 × 5) = 0.01925 cubic meter per minute.

Now, the volume of the conical vessel with base diameter 21 m and depth 12 m will be $\frac{1}{3} \pi r^{2}h = \frac{1}{3} \times (\frac{22}{7}) \times (\frac{21}{2} )^{2} \times 12 = 1386$ cubic meters.

Therefore, the time required to fill the vessel is $\frac{1386}{0.01925 \times 60} = 1200$ hours. (Answer)

Answer 2

Answer:

Time taken = 5 mins

Step-by-step explanation:

Given:

Water flows at the rate of 0.5m/min

Internal radius of the pipe = 2 cm

Radius of the conical vessel = 10 cm

Depth of the conical vessel = 30 cm

To Find:

Time taken to fill the conical vessel

Solution:

First find the volume of water that flows out through the pipe in 1 min.

Here the pipe is in the shape of a cylinder.

Volume of a cylinder is given by,

Volume of a cylinder = π × r² × h

where r is the radius

and h is the height

Here height of the pipe = 0.5 m = 50 cm

Substitute the data,

Volume of water that flows out in 1 min = π × 2² × 50

⇒ 200 π cm³

Now the vessel is in the shape of a cone.

Volume of a cone is given by,

Volume of a cone = 1/3 × π × r² × h

Substitute the given data,

Volume of the cone = 1/3 × π × 10² × 30

Volume of the cone = 1000 π cm³

Now let the conical vessel be filled in x mins.

Hence,

Volume of water that flows out in x mins = Volume of the vessel

Substitute the data,

200 π × x = 1000 π

200 x = 1000

x = 1000/200

x = 5 mins

Hence the time taken to fill the conical vessel is 5 mins.