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# Throwing a ball in a cone that fills with water

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I have a cone of radius 90cm and height 1m.

I have a bowl shaped like a demisphere of radius 10cm.

I have a ball of radius 2cm.

I place the bowl inside the cone.

I throw the ball in the cone.

If it lands inside the bowl, I remove the bowl and the ball, I pour 10ml of water inside the cone, and I place the bowl back (it floats).

If it lands outside of the bowl (in the water), I pick the ball up and do nothing.

Then I repeat this process.

How many times in average will I throw the ball before the cone is full of water?

Jan 6, 2019
edited by Guest  Jan 6, 2019

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We need to know what the probability of you making throwing the ball into the bowl when there is a certain volume of water inside the cone. We also need to know if the ball will go in or out of the bowl if the ball is thrown straight onto the rim.

I think I need more information to solve this problem, but I can provide some help.

The area of a cone is $$\dfrac{1}{3}\pi r^2 h$$.  The radius of this cone is 0.9 m, and the height is 1m. The volume of the cone is $$0.27\pi$$, which is around 0.85 m^3. Since 1 cm^3 = 1 mL^3, and you pour 10mL each time you make the ball into the bowl, you will need to make the ball into the bowl 9 times for the cone to fill up with water.

If the probaility that you make the ball into the bowl each time is P, and X is the number of times you need to throw the ball before the cone is full of water, your equation would be P*X = 9.