The dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
What is surface area?
The surface area of a solid object could be a live of the full area that the surface of the article occupies.
Main body:
The surface area of the closed cylinder is given by,
S = 2πr²+2πrh
And volume is given by,
V = πr²h
Where, R is radius and h is height of cylinder.
Volume is given to be 6 cm³.
V = πr²h = 6
h = 6/πr²
Inserting this value of h in Surface area equation, we get,
S = 2πr²+ 2πr ( 6/πr²)
S = 2πr² + 12 /r
Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,
4πr = 12/r²
r = (3/π)¹/³
r = 0.98 cm approx.
h = 6/π *(0.98)²
h = 6/3.017
h = 1.998 cm
Hence ,the dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
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