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
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V of the sphere = cc
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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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. (6²+8²=10²)
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
