document.write( "Question 1181733: The diameter of the base of a right circular cone is 10 in., and its altitude is 8 in. Find the volume of the largest sphere that can be cut from the cone. \n" ); document.write( "

Algebra.Com's Answer #811662 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "In cross section, the diagram will be a circle inscribed in an isosceles triangle with base 10 and height 8; the center of the sphere (circle in the cross section) is the same distance from all three sides of the triangle.

\n" ); document.write( "Draw the figure, showing the altitude of the triangle and the three radii from the center of the circle to the three sides of the triangle.

\n" ); document.write( "In your diagram there is a right triangle with short leg length 5, long leg 8, and hypotenuse sqrt(89).

\n" ); document.write( "And there is a second right triangle, similar to the first because of equal angles, that has short leg equal to the radius of the circle and hypotenuse equal to 8 minus the radius of the circle.

\n" ); document.write( "Find the radius of the circle (sphere) using the known lengths of the short leg and hypotenuse of those two similar triangles.

\n" ); document.write( " $\"%288-r%29%2Fr+=+sqrt%2889%29%2F5\"$
\n" ); document.write( " $\"r%2Asqrt%2889%29=5%288-r%29\"$
\n" ); document.write( " $\"r%2Asqrt%2889%29+=+40-5r\"$
\n" ); document.write( " $\"r%28sqrt%2889%29%2B5%29=40\"$
\n" ); document.write( " $\"r+=+40%2F%28sqrt%2889%29%2B5%29\"$

\n" ); document.write( "Do that calculation to find the radius of the circle(sphere); then use that radius in the formula for the volume of a sphere to find the answer to the problem.

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\n" ); document.write( "Note my answer to 2 decimal places is 89.15

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