Calculating Radius & Water Depth of a Spherical Bowl

[Chijioke]

The water level in a spherical bowl has a diameter of 30 cm. If the horizontal diameter of the bowl is 10 cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl.
I managed to draw a diagram below:

In my drawing, I am seeing the sphere ABCD as the spherical bowl and the AB as the diameter of the water level.
I also see CD as the horizontal diameter of bowl which is below the water level and d as depth of the water.
If think I am having problem interpreting the problem based on what I have drawn.

 

[erobz]

The water level in a spherical bowl has a diameter of 30 cm. If the horizontal diameter of the bowl is 10 cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl.
I managed to draw a diagram below:
View attachment 321836
In my drawing, I am seeing the sphere ABCD as the spherical bowl and the AB as the diameter of the water level.
I also see CD as the horizontal diameter of bowl which is below the water level and d as depth of the water.
If think I am having problem interpreting the problem based on what I have drawn.

The cross section 10 cm below the water level is the has the diameter of the sphere. The cross section at water level has a 30 cm diameter.

 

[Lnewqban]

Are you supposed to use the equation of a circle or trigonometry to solve this problem?

 

[Steve4Physics]

You could make this a lot simpler by drawing a 2D diagram (vertical plane through centre). Basically this diagran is:

1) a circle, centre O;
2) a horizontal line, $L_1$ through O (i.e. a horizontal diameter);
3) a horizontal chord, $L_2$, 10cm above $L_1$ and with length 30cm.

The rest should follow using Pythagoras.

 

[Chijioke]

 

[haruspex]

View attachment 327223

Looks good.

 

[scottdave]

So if you're rounding to nearest centimeter, it looks good.

 

[haruspex]

So if you're rounding to nearest centimeter, it looks good.

or even nearest mm.