The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.
Given:
The volume of closed right circular cylindrical cans = 128π cm³
As we know the volume of a cylinder = πr²h
By equating;
πr²h = 128π
h = 128/r²
To get the dimensions of a can with minimum surface area;
S = 2πrh + 2πr
Put h = 128/r²;
Therefore, S(r) = 256π/r + 2πr²
S'(r) = -256π/r² + 4πr
S''(r) = -(2*256π)/r³ + 4π
Now, for S(r) = 0;
r = 4cm
for S''(4) > 0 at r = 4 is minimum point.
Hence,
h = 128π/(π*4*4)
h = 8cm
Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.
To learn more about right circular cylinder click here:
brainly.com/question/28448651
#SPJ4
