document.write( "Question 150915: A cylindrical container has a base area of 100 cm^2 and is 12 cm high. If the container is one-third filled with water, what is the volume of the water in the container? \n" ); document.write( "

Algebra.Com's Answer #110878 by jojo14344(1513) $\"\"$ $\"About$

You can put this solution on YOUR website!
We know the in finding the $\"Volume\"$ of the container = $\"pi%28r%5E2%29h\"$
\n" ); document.write( "The $\"height\"$ is given which is $\"%281%2F3%29%2812cm%29\"$ , but we don't have the radius, $\"r\"$ .
\n" ); document.write( "Since $\"Area\"$ is given, we can get it there, with the formula,
\n" ); document.write( " $\"A=2pi%28r%5E2%29%2B2pi%28r%29h\"$ ---- area on the top and base + area on the sides
\n" ); document.write( " $\"100=2pi%28r%5E2%2B%28rh%29%29\"$
\n" ); document.write( " $\"%28100%2F2pi%29=r%5E2%2Brh\"$
\n" ); document.write( "Substituting & re-arranging,
\n" ); document.write( " $\"r%5E2%2B12r-%2850%2Fpi%29=0\"$
\n" ); document.write( "by Quadratic eqn, $\"x=r\"$ , $\"a=1\"$ , $\"b=12\"$ , $\"c=+-50%2Fpi\"$
\n" ); document.write( " $\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$
\n" ); document.write( " $\"x=%28-12%2B-sqrt%2812%5E2-4%2A1%2A-50%2Fpi%29%29%2F%282%2A1%29\"$
\n" ); document.write( " $\"x=%28-12%2B-sqrt%28144%2B200%2Fpi%29%29%2F2\"$
\n" ); document.write( " $\"x=%28-12%2B-sqrt%28207.66198%29%29%2F2\"$
\n" ); document.write( " $\"x=%28-12%2B-14.41%29%2F2\"$
\n" ); document.write( " $\"x=%28-12%2B14.41%29%2F2\"$ -----> $\"x=1.205\"$
\n" ); document.write( " $\"x=%28-12-14.41%29%2F2\"$ -----> $\"x=-13.205\"$
\n" ); document.write( "USE $\"x=1.205=r\"$
\n" ); document.write( "So $\"V=pi%281.205%5E2%29%2812%2F3%29\"$
\n" ); document.write( " $\"V=5.81%28pi%29\"$ cc
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo \n" ); document.write( "

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