document.write( "Question 826849: The volume of a cone is given by the rule V=1/3pie*R^2*h, where r is the radius of the widest part of the cone and h is the vertical height of the cone. Given that the volume of a cone is 100 cm3 and its radius at the widest point is sqrt12 cm, find the height of the cone, expressing your answer in terms of π. \n" ); document.write( "
Algebra.Com's Answer #498349 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "The volume of a cone is given by the rule \"V=%281%2F3%29%2Api%2Ar%5E2%2Ah\", where r is the radius of the \r\n" );
document.write( "widest part of the cone and h is the vertical height of the cone. \r\n" );
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document.write( "Given that the volume of a cone is 100 cubic cm and its radius at the widest point is \r\n" );
document.write( "\"sqrt%2812%29\" cm, find the height of the cone, expressing your answer in terms of \"%28pi%29\".\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Begin with the formula for the volume of a cone. Check that all measurements are in terms of \r\n" );
document.write( "cm, for length, or cubic cm, for volume. (They are.)\r\n" );
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document.write( "Substitute 100 cubic cm for V and \"sqrt%2812%29\" for r into the formula.\r\n" );
document.write( "\"V=%281%2F3%29%28pi%29%2Ar%5E2%2Ah\"\r\n" );
document.write( "\"%28100%29=%281%2F3%29%28pi%29%2A%28sqrt%2812%29%29%5E2%2Ah\"\r\n" );
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document.write( "Simplify. When you square the square root of 12 you get 12 because one operation undoes \r\n" );
document.write( "the other; 1/3 of 12 is 4.\r\n" );
document.write( "\"%28100%29=%281%2F3%29%28pi%29%2A12%2Ah\"\r\n" );
document.write( "\"%28100%29=4%2A%28pi%29%2Ah\"\r\n" );
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document.write( "Solve for h. Divide both sides of the equation by \"4%2Api\".\r\n" );
document.write( "\"h+=+100%2F%284%2Api%29\"\r\n" );
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document.write( "Simplify. 100 divided by 4 is 25.\r\n" );
document.write( "\"h=25%2F%28pi%29\"\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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