# Math Help - Related rates problem

1. ## Related rates problem

One of the practice problems in my book is giving me trouble.

"A hemispherical bowl of radius 10 cm contains water to a depth of h cm. Find the radius of the surface of the water as a function of h."

I can see that the radius gets smaller as h gets smaller but I'm not how to go about finding an equation. The back of the book says that the answer is r=(20h -h^2)^(1/2) and I think they used the circle equation but I'm not sure. Does anyone have any hints?

2. ## Re: Related rates problem

The bowl has a radius of 10cm. The distance from the height of the water to the top centre of the hemisphere (from where the radius is measured) is $(10-h)$cm

I drew a diagram in front of me for this, and you can do it using Pythagoras.

Draw the hemisphere. Draw the level of the water at any distance $(10-h)$cm below the top and label the $(10-h)$ distance. Then draw a radius from the centre top of the hemisphere to the point on the hemisphere that touches the surface of the water. If you have understood me, you should now have a right triangle. The base is $r$, the height is $(10-h)$ and the hypotenuse is $10$.

I hope you'll forgive me for my dreadful artistic skills, but I have done a diagram here:

Spoiler:

I'll check this in a second, it's sort of a leap of faith on my part, but hopefully you should get the expected result.

Edit: Yeah, I've managed to obtain their solution this way.