Question

6. An empty tank is in the form of an inverted frustrum of a cone having a radii of 1 m and 1.5 m at the bottom and top respectively. It has a height of 2 m. Water is allowed to flow into it at a constant rate of 30 liters per minute. How fast in mm/min is the water rising in the tank when it is 30 cm deep?

Answer 1

Step-by-step explanation:

Diameter of the pipe =5mm=

10

5

cm=

2

1

cm.

∴ Radius of the pipe =

2

1

×

2

1

cm=

4

1

cm.

In 1 minute, the length of the water column in the cylindrical pipe =10m=1000cm.

∴ Volume of water that flows out of the pipe in 1 minute

=π×

4

1

×

4

1

×1000cm

3

Also, volume of the cone =

3

1

×π×20×20×24cm

3

.

Hence, the time needed to fill up this conical vessel

=(

3

20×20×24

×

1000

4×4

)=

30

4×24×16

minutes

=

5

256

minutes=51.2minutes.

Hence, the required time is 51.2 minutes.