document.write( "Question 947652: a ramu tin maker converts cubical metallic box into 10 cylindrical tins.Side of the cube is 50 cm and radius of cylinder is 7 cm, find the height of each cylinder so made,if the wastage of 12% is incurred in the process. \n" ); document.write( "

Algebra.Com's Answer #578635 by KMST(5328) $\"\"$ $\"About$

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Apparently that tin maker can flatten the cubical can into and odd shaped sheet of tin with the same surface area,
\n" ); document.write( "and then manage to cut from that sheet the necessary pieces to make the 10 cylindrical cans, wasting only 12% of the material.
\n" ); document.write( "The total surface area of a cube with a $\"50cm\"$ side is
\n" ); document.write( " $\"6%2850cm%29%5E2=6%2A%282500cm%5E2%29=15000cm%5E2\"$ .
\n" ); document.write( "Wasting $\"%2212%25%22\"$ means using $\"%22100%25%22-%2212%25%22=%2288%25%22=88%2F100=0.88\"$ .
\n" ); document.write( " $\"%2288%25%22\"$ of $\"15000cm%5E2\"$ is
\n" ); document.write( " $\"0.88%2A15000cm%5E2=13200cm%5E2\"$ .
\n" ); document.write( "The total surface area of a cylinder with a $\"7cm\"$ radius and a height of $\"h\"$ $\"cm\"$ is
\n" ); document.write( " $\"2%2Api%2A%287cm%29%5E2%2B2%2Api%2A%287cm%29%2Ah\"$ $\"cm=2%2Api%2A7%2A%287%2Bh%29\"$ $\"cm%5E2=14pi%2A%287%2Bh%29\"$ $\"cm%5E2\"$ .
\n" ); document.write( "The total surface area of $\"10\"$ such cylinders is
\n" ); document.write( " $\"140pi%287%2Bh%29\"$ $\"cm%5E2\"$ .
\n" ); document.write( "Since that is supposed to be the $\"13200cm%5E2\"$ used, our equation is
\n" ); document.write( " $\"140pi%287%2Bh%29=13200\"$
\n" ); document.write( "Solving for $\"h\"$ :
\n" ); document.write( " $\"140pi%287%2Bh%29=13200\"$
\n" ); document.write( " $\"7%2Bh=13200%2F140pi\"$
\n" ); document.write( " $\"h=13200%2F140pi-7\"$
\n" ); document.write( "The approximate solution is $\"highlight%28h=23.012%29\"$ $\"cm\"$ . \n" ); document.write( "

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