A plane intersects a sphere to form a circle as shown in the figure. The distance from the center of the circle to the center of the sphere is 10in. If the area of the circle formed by the intersection is 576 pi inches squared, what is the volume of the​ sphere?

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A plane intersects a sphere to form a circle as shown in the figure. The distance from the center of the circle to the center of the sphere is 10in. If the area of the circle formed by the intersection is 576 pi inches squared, what is the volume of the​ sphere?

Mathematics
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|dw:1443066944419:dw|
I'm totally lost on this one, I keep getting similar problems wrong, the last equaled out to 4000/3 pi in.^3

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Hey if psble could you attach the original diagram
I'm finding it a bit hard to relate the word problem to the picture that you have drawn
the picture i drew is pretty much it.
|dw:1443067700784:dw|
Ok got you
It wants me to find the volume, I even tried the V=4/3*3.14*r^3
Think of the given diagram as a small spherical fish tank, 10cm represents the center of top surface to the center of fish tank : |dw:1443067804228:dw|
They gave you surface area of the top surface : \(576\pi\) Say, the radius of top surface is \(r\) : |dw:1443067992574:dw|
r=10 ?
\[\pi r^2 = 576\pi\] solve \(r\)
r=24 ?
Yes, the radius of top circular disk surface is \(24\) : |dw:1443068220493:dw|
Next, see if you can find the radius of sphere : |dw:1443068276532:dw|
would I substitute 24 as r into the same equation?
do you see a right triangle with sides \(10, 24, R\) ? you need to setup an equation and find the value of \(R\)
which equation would I use? A=1/2 bh? sorry....
when you see a right triangle, you should think of "pythagoras theorem"
10^2+24^2=676
yes take square root
\[\sqrt{676} =26\]
@ganeshie8 What do I do next?
so \(26\) is the radius of sphere
use volume formula of sphere and finish it off
V=4/3*3.14*26^3 ?
I get a huge number 73584.85
Looks good!

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