Find the dimensions and volume of a cylinder of maximum volume, given that 600pi square inches is to be used?

Question

including the base and the lid

Answer 1

The surface area of the cyclinder equals 600π inches squared.

The equation for the surface area of a cylinder is

S = 2πrh + 2πr² = 600π inches squared

Solve for h.

V = πr²h

Substitute what you found for 'h' in the first part into the volume equation then take the derivative with respect to 'r'. You should get this equation.

dV/dr = 300π - 3πr²

Solve for 'r' with dV/dr = 0 to find the maximum volume.
Solve for 'h' using the 'r' value you find.

The answers should be

r = 10
h = 20
V = 2000π inches squared

Answer 2

radius=10
height=20
v=pi r^2*h=19,739.24 cubic inches. just to clarify V=pr^2h, let p stand for pi. Surface area = 2prh+2pr^2 and that = 600p in.^2
solve for h = (300-r^2)/r. substitute into V formula
V=pr^2(300-r^2)/r = pr(300-r^2)
dv/dr = 300p - 3pr^2=0, 100=r^2, r=10
h=(300-r^2)/r = 20
V=p*r^2*h =2000p=6280 in^3