document.write( "Question 1135970: A right circular cone sits on a table, pointing up. The cross-section triangle, perpendicular to the base, has a vertex angle of 60 degrees. The diameter of the cone's base is 12\sqrt{3} inches. A sphere is placed inside the cone so that it is tangent to the sides of the cone and sits on the table. What is the volume, in cubic inches, of the sphere? Express your answer in terms of $\pi$. \n" ); document.write( "

Algebra.Com's Answer #753706 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Since the vertex angle of the cone is 60°, the cross-section triangle is\r\n" );
document.write( "an equilateral triangle, with all sides equal in length, and each interior\r\n" );
document.write( "angle equaling 60°.\r\n" );
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document.write( "The volume of the sphere is .\r\n" );
document.write( "So we need only find the radius r and substitute.\r\n" );
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document.write( "Triangle AOB is a 30°-60°-90° right triangle, so the longer leg is √3 times\r\n" );
document.write( "the shorter leg, so:\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "Take positive square root of both sides:\r\n" );
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document.write( "Substitute 4 for r in\r\n" );
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document.write( " cubic inches  <--Volume of the sphere.\r\n" );
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document.write( "Edwin

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