SOLUTION: Hey, im having a hard time with the question im on..please help. A glass ball shown below has a diameter of 30 in. Ms. Ping removed a horizontal slice from the bottom of the ball,

Algebra ->  Volume -> SOLUTION: Hey, im having a hard time with the question im on..please help. A glass ball shown below has a diameter of 30 in. Ms. Ping removed a horizontal slice from the bottom of the ball,      Log On


   

Question 599172: Hey, im having a hard time with the question im on..please help.
A glass ball shown below has a diameter of 30 in. Ms. Ping removed a horizontal slice from the bottom of the ball, to use as a fishbowl. If the radius of the flat surface formed by the cut is 9in., what is the current height of the ball?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It's always a good idea to draw this if you have no idea what's going on. So start with a 3D sphere. Next draw the cross section of the sphere (which will be a circle).

Now construct a chord on the bottom of the circle to represent the cut. Half of this length is the radius of the circle which represents the hole in the fishbowl.

Now draw in two radii: one cuts the chord in half and the other connects the center of the sphere with the edge of the chord. This is all shown below



Note: be sure to label the drawing. In this case, I'm letting x be the height of the ball (with that lower bit cut of)

We can see that a triangle forms. Not just any triangle, but a right triangle.

So we can use the pythagorean theorem to solve.

a^2 + b^2 = c^2

(9)^2 + x^2 = (15)^2

81 + x^2 = 225

x^2 = 225 - 81

x^2 = 144

x = sqrt(144)

x = 12


So the height of the bowl is 12 inches.