You are given a metal sphere of radius R. You are required to recast the solid into smaller solid spheres to increase the total surface area as much as possible. The number of final products is unlimited. Suggest what you would do.
(Hint: Recasting the solid into 2 smaller spheres of equal radii gives a 26% increase in its surface area.)
About area and volume
2009-07-20 3:24 am
回答 (1)
2009-07-20 3:46 am
✔ 最佳答案
The volume of the original sphere is (4/3)πR^3 and its surface area is 4πR^2The volume of the new sphere is (4/3)πr^3 and its surface area is 4πr^2
Since (4/3)πR^3=N(4/3)πr^3
=>R^3=Nr^3
Sub into 4πr^2=4πR^2/(N^2/3)
The total surface area is 4πR^2/(N^2/3)*N=4πR^2(N^1/3)
When n=2,N^1/3=1.26 and gives a 26% increase in its surface area.
So, you should make a new sphere as small as possible !!!
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