document.write( "Question 999085: A cylinda CYLINDER and sphere both have the same diameter and the same volume.if the height of the cylinder is 36cm, find their common radius. \n" ); document.write( "
Algebra.Com's Answer #616778 by addingup(3677)\"\" \"About 
You can put this solution on YOUR website!
Volumes: cylinder= pi*r^2*h sphere= 4/3pi*r^3
\n" ); document.write( "Let's rewrite the cylinder this way: h*pi*r^2
\n" ); document.write( "36*pi*r^2= 4/3pi*r^3
\n" ); document.write( "subtract 4/3pi*r^3 from both sides
\n" ); document.write( "36*pi*r^2-4/3pi*r^3= 0 Now factor the left:
\n" ); document.write( "-4/3pi*r^2(r-27)= 0 Divide both sides by -4/3pi to simplify:
\n" ); document.write( "r^2(r-27)= 0 (of course, you divided the zero by -4/3pi but zero divided by any number is 0).
\n" ); document.write( "Split into 2 equations:
\n" ); document.write( "r-27= 0 or r^2= 0 on the left, add 27 on both sides and on the right take the square root on both sides:
\n" ); document.write( "Your answer:
\n" ); document.write( "r= 27 or r= 0 Throw away the 0, your answer is 27
\n" ); document.write( "Proof:
\n" ); document.write( "pi*27^2*36= 4/3pi*27^3 Do it in your calculator, I've run out of time but I'm sure you will find that the equality is true, meaning we've got the right answer. \n" ); document.write( "
\n" );