Find the time required for a cylindrical tank of radius 2.5 m and height 3 m to empty through a round hole of 2.5 cm with a velocity `2. 5sqrt(h)` m/s, `h` being the depth of the water in the tank.

Explanation

To solve the problem of finding the time required for a cylindrical tank to empty through a hole, we can follow these steps:

### Step 1: Understand the problem
We have a cylindrical tank with a radius of 2.5 m and a height of 3 m. The water flows out through a hole with a radius of 2.5 cm, and the velocity of the water flowing out is given by \( v = 2.5 \sqrt{h} \), where \( h \) is the depth of the water in the tank.

### Step 2: Set up the volume equations
The volume of water that decreases in the tank when the height decreases by \( dh \) is given by:
\[
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