A solid 2 cm cable of length 20 m is dropped into a cylindrical tank of diameter 5 m which is half full of water. How much will the liqud level in the cylinder rise?

Question

please explain method to solve

Answer 1

Hello, Bran,

This is an updated answer, thanks to Aries H., who commented that something was wrong. I mistakenly used 5m as the cable diameter. It should have been 2 cm. Wow. Rather than going in detail, I have the calculation summary:

Cable: Volume = 0.006283 m³

Tank: Volume, assuming a 1 meter height: 19.6345 m³

New Volume: 19.6412 m³

New Tank Height: 1.00032 m

Increase in height: 0.00032 m, or 0.032 cm

The volume of a cylinder is V = πr²h. Use this formula for both the cable and the tank. I assumed a random tank height of 1 meter. We are calculating a change in height, not the total, so a value of 1 meter is fine. Convert all dimensions to meters (100cm = 1 meter) and calculate volumes of both the tank and cable. Add the two numbers to find the new total volume of water and cable, then use h = V/πr² to calculate the new height. The difference of this with 1 meter is 0.00032m, or 0.032cm.

Bob