You want to build a closed cylinder (i.e. a tube with two circular end pieces) that has a total surface area of 80cm2.

cm2. The radius of the cylinder will ber, and the heighth (in cm)

hcm.

(a cylinder has volumeV=r^2h cm^3 and surface area=A=2r^2+2rhcm^2.)

(a) Find the radius of such a cylinder for which thevolume is maximized: (units cm)

(b) Find the maximum volume of the cylinder: (units cm^3)

answer using 5 significant digits.