anonymous one year ago 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?

1. anonymous

|dw:1443066944419:dw|

2. anonymous

@ganeshie8 @mathstudent55 @Zale101 @kohai @dan815 @zepdrix

3. anonymous

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

4. ganeshie8

Hey if psble could you attach the original diagram

5. ganeshie8

I'm finding it a bit hard to relate the word problem to the picture that you have drawn

6. anonymous

the picture i drew is pretty much it.

7. anonymous

|dw:1443067700784:dw|

8. ganeshie8

Ok got you

9. anonymous

It wants me to find the volume, I even tried the V=4/3*3.14*r^3

10. 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|

11. ganeshie8

They gave you surface area of the top surface : $$576\pi$$ Say, the radius of top surface is $$r$$ : |dw:1443067992574:dw|

12. anonymous

r=10 ?

13. ganeshie8

$\pi r^2 = 576\pi$ solve $$r$$

14. anonymous

r=24 ?

15. ganeshie8

Yes, the radius of top circular disk surface is $$24$$ : |dw:1443068220493:dw|

16. ganeshie8

Next, see if you can find the radius of sphere : |dw:1443068276532:dw|

17. anonymous

would I substitute 24 as r into the same equation?

18. ganeshie8

do you see a right triangle with sides $$10, 24, R$$ ? you need to setup an equation and find the value of $$R$$

19. anonymous

which equation would I use? A=1/2 bh? sorry....

20. ganeshie8

when you see a right triangle, you should think of "pythagoras theorem"

21. anonymous

10^2+24^2=676

22. ganeshie8

yes take square root

23. anonymous

$\sqrt{676} =26$

24. anonymous

@ganeshie8 What do I do next?

25. ganeshie8

so $$26$$ is the radius of sphere

26. ganeshie8

use volume formula of sphere and finish it off

27. anonymous

V=4/3*3.14*26^3 ?

28. anonymous

I get a huge number 73584.85

29. ganeshie8

Looks good!