Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A well of radius is dug deep. The earth taken out is spread evenly to make a ring-shaped bank round the well. The bank is wide. Find the height of the bank.
Water from a pipe of radius at speed in time is . The time to fill a tank is its volume divided by the volume per second. Earth from a well is , and a layer of area has height volume . A solid under water raises the level by its volume divided by the surface area of the water.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The earth. .
Step 2. The ring. The outer radius is . The area is .
Step 3. The height. .
Check. The answer does not use , because it cancels.
Answer: the bank is high.
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