# Water Level Puzzle - Solution

### The Puzzle:

There's a toy boat floating in a pool.

Place a lead ball in the boat (without sinking it), and measure the level of water in the pool.

Now take the ball out of the toy boat and drop it into the pool, and measure the water's level again.

Will the two water level measurements be different, if so which will be higher?

Place a lead ball in the boat (without sinking it), and measure the level of water in the pool.

Now take the ball out of the toy boat and drop it into the pool, and measure the water's level again.

Will the two water level measurements be different, if so which will be higher?

### Our Solution:

The water's level will be higher when the ball is in the boat.

When the ball is in the boat, it displaces the volume of water that weighs the same as the ball.

When the ball is in the water, it only displaces as much water as its volume.

For example, if the lead ball's volume is 1 ml, then its mass will be 11.3 g, which means it will force the boat to displace 11.3 ml of water.

But when the ball is in the water, it only displaces its own volume of 1 ml.

More water is displaced when the ball is in the boat, and so the water level rises more, leading to our result.

When the ball is in the boat, it displaces the volume of water that weighs the same as the ball.

When the ball is in the water, it only displaces as much water as its volume.

For example, if the lead ball's volume is 1 ml, then its mass will be 11.3 g, which means it will force the boat to displace 11.3 ml of water.

But when the ball is in the water, it only displaces its own volume of 1 ml.

More water is displaced when the ball is in the boat, and so the water level rises more, leading to our result.

*See this puzzle without solution*

*Discuss this puzzle at the Math is Fun Forum*