water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 6 metres per second into a cylindrical tank. the radius of whose base is 60 cm. find the rise in the level of water in 30 minutes

To find the rise in the level of water in the tank, we need to determine the volume of water flowing into the tank in 30 minutes.

First, let's calculate the cross-sectional area of the circular pipe:
The internal diameter is given as 2 cm, so the radius (r) of the pipe is half of the diameter, which is 1 cm.
The cross-sectional area (A) of a circular pipe is given by the formula: A = π * r^2.
In our case, A = π * (1 cm)^2 = π cm^2.

Next, let's determine the volume of water flowing out of the pipe per second:
The rate of flow is given as 6 meters per second. However, the cross-sectional area we calculated is in square centimeters. Hence, we need to convert the rate of flow to cubic centimeters per second.
To do this, we need to multiply the rate of flow by the cross-sectional area: 6 * π cm^2/s.

Now, let's find the volume of water flowing out of the pipe per minute:
There are 60 seconds in a minute. So, in one minute, the volume of water flowing out would be: 6 * π cm^2/s * 60 s/min = 360 * π cm^3/min.

To find the volume of water flowing out in 30 minutes:
We need to multiply the volume per minute by 30: 360 * π cm^3/min * 30 min = 10,800 * π cm^3.

Finally, let's calculate the rise in the level of water in the tank:
The volume of water required to cause a rise in the level of water is equal to the volume of the cylindrical tank.
The formula to calculate the volume of a cylinder is: V = π * r^2 * h, where r is the radius of the base of the cylinder and h is the height/rise in the level of water.
In our case, V = how much water is required to cause a rise in the level = π * (60 cm)^2 * h.

Setting the volume of water flowing into the tank (10,800 * π cm^3) equal to the volume required to cause a rise in the level (π * (60 cm)^2 * h), we can solve for h:
10,800 * π = π * (60 cm)^2 * h
Dividing both sides by π:
10,800 = (60 cm)^2 * h
Solving for h:
h = 10,800 / (60 cm)^2

Calculating this, we find:
h ≈ 3 cm (rounded to the nearest whole number)

Therefore, the rise in the level of water in the tank is approximately 3 cm.