Question

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

Answer 1

Answer:  51.2 minutes.

Step-by-step explanation:  

Let the radius of cylindrical pipe be r.

Suppose the radius and height of the conical vessel be R and H respectively.

∴

r =  

1

4

cm

2R = 40 cm

∴ R = 20 cm

and H = 24 cm

Volume of conical vessel =  

1

3

π

R

2

H  =  

1

3

×

π

×  

20

2

 × 24    

c

m

3

Rate of water flow = 10 m/min = 1000 cm/min    

∴ Volume of water flowing out of the pipe in one minute =  

π

 

r

2

× 1000 cm =  

π

× (

1

4

)

2

× 1000  

c

m

3

Let the time taken to fill the conical vessel be t minutes.    

∴ Volume of water flowing out of the pipe in tminutes =  

π

× (

1

4

)

2

× 1000  

c

m

3

Volume of water flowing out of the pipe in tminutes = Volume of conical vessel

π

 

1

16

× 1000 t =  

1

3

 

π

400 × 24

t =  

400

×

24

×

16

3

×

100

= 51.2

Thus, the time taken to fill the conical vessel is 51.2 minutes.