ANOTHER FUNCTION HELP......THESE NEVER SEEM TO GIVE U INFO

[sungjin6458]

Q. A can in the shape of a right circular cylinder is required to have a volume of 250 cubic centimeters.
a. express the amount of A of matureial to make the can as a function of the radius r of the cylinder.
b. how much material is required if the can is of radius 3 centimeters?
c. how much material is required if the can is of radius 5 centimeters?
d. graph A=A(r). for wat value of r is A smallest?

So far....(man i dont get this at all...plz dont think im stuppid lol)
a. area of base * height = 250 cubic centimeters ?
b.just plug in...right?
c.just plug in...right?
d. i can graph it...but tell me why does it say graph A=A(r)? is it the same thing as graphing the equation from part a?


thx...this website has been alot of help for me as for many of my friends they appreciate the help

 

[galactus]

The amount of material of the can can be expressed as the surface area of a cylinder plus the top and bottom, which is 2 circles. Right?.

So we have \(\displaystyle 2{\pi}r^{2}+2{\pi}rh\). [1]

The volume of the can is to be: \(\displaystyle {\pi}r^{2}h=250.\) [2]

To get part a, solve [2] for h and sub into [1]; differentiate, set equal to 0 and

solve for r to get part d. That will be the value of r for which A will be least. You

will find that the minimum occurs when the height of the can is equal to the

diameter of the base. Parts b and c are just a matter of subbing into the equation