calculate the dimensions of a cylindrical can that would provide the minimum surface area if the volume is 525 cm ^3

Answer 1

V= 525 = hpi(r^2) = height times area of top or bottom

h= 525/pi(r^2)

Surface Area = A = 2pirh + 2pir^2 = area of side + area of top & bottom plus

A = 2pir(525/pir^2 + 2pir^2

A = 1050/r +2pir^2 take the derivative and set equal to zero, solve for radius

A' -1050/r^2 +4pir =0

-1050 +4pit^3 = 0

r^3 = 525/2pi

r = (525/2pi)^1/3

r= 4.372 cm = radius

diameter = 2r = 8.7 cm

h= 525/pir^2 = 8.7 cm = height