# 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 21 m and depth 12 m.

### Asked by deep_72 | 28th Feb, 2011, 07:02: PM

Expert Answer:

### Dear student,
We have:
r = radius of the base of the conical vessel = 21/2 m
h =height of the conical vessel = 12 m
So, volume of the conical vessel = 1/3 × 22/7 × 21/2 × 21/2 × 12... (1)
Suppose the conical vessel is filled in x minutes.
Then, length if the water coloumn = 5x m
Clearly, water column forms a cylinder of length 5x m, and radius 7/ 2 cm = 7/ 200 m
So, volume of water that flows in x minutes is given by:
22/7 × 7/200 × 7/200 × 5x.....(2)
Equate equations (1) and (2) to get the required value of x.

We hope that clarifies your query.
Regards,
Team
TopperLearning

### Answered by | 30th Nov, 2017, 02:34: PM

## Related Videos

- From a cylindrical wooden log of length 30 cm and base radius 7 root 2 cm, biggest cuboid of square base is made. Find the volume of wood wasted.
- A cube of copper edge 11cm is melted and formed into a cylindrical wire of diameter 0.5cm. what length of wire will be obtained from the cube
- A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm .If the bowl is filled with soup to a height of 4 cm ,how much soup the hospital has to prepare daily to serve 250 patients ?
- The circumference of the base of a cylindrical vessel of height 28 cm is 352 cm. Find the amount of water it can hold.
- A rectangular piece of paper 33 cm long and 16 cm wide is rolled along its breadth to get a cylinder of height 16 cm. Find the volume of the cylinder.
- A cylindrical vessel of diameter 84 cm and height 18 cm contains milk. This milk is to be filled in cylindrical tumblers of radius 7 cm and height 6 cm. Find the number of tumblers that can be filled with milk.
- A solid rectangular block of iron of dimensions 7 cm x 4 cm x 2.75 cm is recast into a cylinder of radius 7 cm. Find the height of the recast cylinder.
- A cylindrical bucket of diameter 28 cm and height 12 cm is full of water. The water is emptied into a rectangular tub of length 66 cm and breadth 28 cm. Find the height to which water rises in the tub.
- A rod 2 m in length and 1.2 cm in radius is drawn into another rod of length 72 cm. Find the radius of the new rod.
- Rain water falls in a tub of dimensions 6 m x 4 m x 2.75 m and is transferred to a cylindrical tub of radius 10 meters. Find the height of water in the cylindrical tub.

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change