Math, asked by jatin229, 1 year ago

water flows at rate of 10m/minute through a cylindrical pipe of 5mm in diameter. how long would it take to fill a conical vessel whose diameter of base is 40 cm and depth is 24 cm?

Answers

Answered by paul4917
6
so time taken is 153.6minute
Attachments:
Answered by AngelGem
0

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.

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