anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1443066944419:dw|
anonymous
  • anonymous
@ganeshie8 @mathstudent55 @Zale101 @kohai @dan815 @zepdrix
anonymous
  • anonymous
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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ganeshie8
  • ganeshie8
Hey if psble could you attach the original diagram
ganeshie8
  • ganeshie8
I'm finding it a bit hard to relate the word problem to the picture that you have drawn
anonymous
  • anonymous
the picture i drew is pretty much it.
anonymous
  • anonymous
|dw:1443067700784:dw|
ganeshie8
  • ganeshie8
Ok got you
anonymous
  • anonymous
It wants me to find the volume, I even tried the V=4/3*3.14*r^3
ganeshie8
  • ganeshie8
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|
ganeshie8
  • ganeshie8
They gave you surface area of the top surface : \(576\pi\) Say, the radius of top surface is \(r\) : |dw:1443067992574:dw|
anonymous
  • anonymous
r=10 ?
ganeshie8
  • ganeshie8
\[\pi r^2 = 576\pi\] solve \(r\)
anonymous
  • anonymous
r=24 ?
ganeshie8
  • ganeshie8
Yes, the radius of top circular disk surface is \(24\) : |dw:1443068220493:dw|
ganeshie8
  • ganeshie8
Next, see if you can find the radius of sphere : |dw:1443068276532:dw|
anonymous
  • anonymous
would I substitute 24 as r into the same equation?
ganeshie8
  • ganeshie8
do you see a right triangle with sides \(10, 24, R\) ? you need to setup an equation and find the value of \(R\)
anonymous
  • anonymous
which equation would I use? A=1/2 bh? sorry....
ganeshie8
  • ganeshie8
when you see a right triangle, you should think of "pythagoras theorem"
anonymous
  • anonymous
10^2+24^2=676
ganeshie8
  • ganeshie8
yes take square root
anonymous
  • anonymous
\[\sqrt{676} =26\]
anonymous
  • anonymous
@ganeshie8 What do I do next?
ganeshie8
  • ganeshie8
so \(26\) is the radius of sphere
ganeshie8
  • ganeshie8
use volume formula of sphere and finish it off
anonymous
  • anonymous
V=4/3*3.14*26^3 ?
anonymous
  • anonymous
I get a huge number 73584.85
ganeshie8
  • ganeshie8
Looks good!

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