Asked by Anonymous
What is the least amount of material that can be used to make a soup can with circular base and closed top with capacity 6 cubic inches?
Answers
Answered by
Reiny
Let the radius be r
and the height be h inches
V= πr^2 h
h =6/(πr^2)
SA = 2πr^2 + 2πrh
= 2πr2 + 2πr(6/(πr^2)
= 2πr^2 + 12/r
d(SA)/dr = 4πr - 12/r^2
= 0 for a max or min
4πr = 12/r^2
4πr^3 = 12
r^3 = 3/π
r = ...
sub back into SA
check my arithmetic
and the height be h inches
V= πr^2 h
h =6/(πr^2)
SA = 2πr^2 + 2πrh
= 2πr2 + 2πr(6/(πr^2)
= 2πr^2 + 12/r
d(SA)/dr = 4πr - 12/r^2
= 0 for a max or min
4πr = 12/r^2
4πr^3 = 12
r^3 = 3/π
r = ...
sub back into SA
check my arithmetic
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