SOLUTION: A sphere is just fit in a cone such that it is the largest sphere that can be fit into that sphere. The height of cone is 8 cm and radius of cone is 6 cm. Find the volume of the sp

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Question 1017561: A sphere is just fit in a cone such that it is the largest sphere that can be fit into that sphere. The height of cone is 8 cm and radius of cone is 6 cm. Find the volume of the sphere.
Found 3 solutions by Alan3354, ikleyn, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A sphere is just fit in a cone such that it is the largest sphere that can be fit into that sphere. The height of cone is 8 cm and radius of cone is 6 cm. Find the volume of the sphere.
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Find the radius of the sphere.
Use a triangle with a base of 12 cm and a height of 8 cm.
--> a triangle with sides of 10, 10 & 12 cm.
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There are various ways to find r of the inscribed circle.
r = 3
----
V of the sphere = cc

Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
A sphere is just fit in a cone such that it is the largest sphere that can be fit into that sphere. The height of cone is 8 cm and radius of cone is 6 cm. Find the volume of the sphere.
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See the lesson Solved problems on volume of spheres in this site.

Very similar problem was solved there (Problem 5) with detailed explanations.


Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!
Here is a drawing of the mid-cross section of the 
largest sphere in the cone, which is the largest 
circle inside triangle ABC:



Right triangles ADC and OEC are similar because they share
a common angle at A.

The hypotenuse of ADC is AC.  And AC = 10 by the Pythagorean 
theorem applied to triangle ADC. (6+8=10)



So:



Cross-multiply and solve that and get r = 3

So the radius of the circle is 3, which is also the radius of
the sphere.

The volume of a sphere is given by the formula





 cubic centimeters.

Edwin
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