Geometry question using Pythagoras’ Theorem?

[Ocean]

A bowl is in the shape of a hemisphere (half sphere) with radius 10cm. The surface of the water in the container has a radius of 7cn. How deep is the water? Round answer to two decimal places.

The answer is 2.86cm but I don't know how to get to it?

 

[lev888]

Could you draw and post the cross-section (through the center of the bowl) of this setup with all given dimensions?

 

[MarkFL]

Consider the following diagram:



\(d\) is the quantity we want. Can you see that:

[MATH]y^2+7^2=10^2[/MATH]
[MATH]y+d=10[/MATH]

 

[Ocean]

Consider the following diagram:

View attachment 12005

\(d\) is the quantity we want. Can you see that:

[MATH]y^2+7^2=10^2[/MATH]
[MATH]y+d=10[/MATH]

Thank you so much!! The diagram’s really helpful!

 

[MarkFL]

Okay, you should get (in cm):

[MATH]d=10-\sqrt{51}\approx2.8585715714571496[/MATH]