The surface area of a cylinder is 800 cm2 . What are the radius and height of the cylinder if it has the greatest volume possible?

Answer 1

surface area = 800 cm^3 = 2hpir +2pir^2 = height times the circumference + twice the base

400 = hpir + pir^2

400/pir = h+r

h = 400/pir -r

V = hpir^2

= (400/pir -r)pir^2 = 400r - pir^3

V' = 400 -3pir^2=0

r^2 = 400/3pi

r = 20/sqr3pi = about 7.00 cm

h = 400/pir - r = 400(sqr3pi/20) - 20/sqr3pi

h = 20sqr3pi - 20/sqr3pi = about 133.07 cm

about 7 by 133 cm gives the greatest volume