Asked by Yuni
the volume of an cylindrical can with a radius r cm and height h cm is 128000 c^3, show that the surface area of the can is A=2(22/7)r^2 + 246000/r. Find the value for r to minimize the surface area.
*i know what the quest. ask but i do not know how to apply it.
*i know what the quest. ask but i do not know how to apply it.
Answers
Answered by
drwls
It looks like you are being asked to use 22/7 for pi. In that case,
2(22/7)r^2 is the combined area of the two circular ends.
If the volume is V = pi*r^2*h, the curved cylindrical area is
2 pi*r*h = 2V/r.
That is where your 246000/r term comes from.
To minimize the surface area, set the derivative of A(r) equal to zero.
dA/dr = (88/7) r -246,000/r^2 = 0
r = (246,000*7/88)^1/3 = 26.9 cm
If you have not yet studied differential calculus, I suggest you graph A vs r and see where it is a mininum.
2(22/7)r^2 is the combined area of the two circular ends.
If the volume is V = pi*r^2*h, the curved cylindrical area is
2 pi*r*h = 2V/r.
That is where your 246000/r term comes from.
To minimize the surface area, set the derivative of A(r) equal to zero.
dA/dr = (88/7) r -246,000/r^2 = 0
r = (246,000*7/88)^1/3 = 26.9 cm
If you have not yet studied differential calculus, I suggest you graph A vs r and see where it is a mininum.
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