SOLUTION: 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 wa

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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.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Apparently that tin maker can flatten the cubical can into and odd shaped sheet of tin with the same surface area,
and then manage to cut from that sheet the necessary pieces to make the 10 cylindrical cans, wasting only 12% of the material.
The total surface area of a cube with a 50cm side is
6%2850cm%29%5E2=6%2A%282500cm%5E2%29=15000cm%5E2 .
Wasting %2212%25%22 means using %22100%25%22-%2212%25%22=%2288%25%22=88%2F100=0.88 .
%2288%25%22 of 15000cm%5E2 is
0.88%2A15000cm%5E2=13200cm%5E2 .
The total surface area of a cylinder with a 7cm radius and a height of hcm is
2%2Api%2A%287cm%29%5E2%2B2%2Api%2A%287cm%29%2Ahcm=2%2Api%2A7%2A%287%2Bh%29cm%5E2=14pi%2A%287%2Bh%29cm%5E2 .
The total surface area of 10 such cylinders is
140pi%287%2Bh%29cm%5E2 .
Since that is supposed to be the 13200cm%5E2 used, our equation is
140pi%287%2Bh%29=13200
Solving for h :
140pi%287%2Bh%29=13200
7%2Bh=13200%2F140pi
h=13200%2F140pi-7
The approximate solution is highlight%28h=23.012%29cm .