This is a problem that has been torturing me for about 45 minutes now and I don't know how to complete it, please help!
A cylindrical can has a volume of 400(pi) cm cubed. The material for the top and bottom costs $.02 per square centimeter. The material for the vertical surface costs $.01 per square centimeter. Express the cost C of the materials to make the can as a function of the radius r.
Can you please explain this to me? Thank you for all the help guys, it's much appreciated
A cylindrical can has a volume of 400(pi) cm cubed. The material for the top and bottom costs $.02 per square centimeter. The material for the vertical surface costs $.01 per square centimeter. Express the cost C of the materials to make the can as a function of the radius r.
Can you please explain this to me? Thank you for all the help guys, it's much appreciated
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What you need to do is find surface area of the top and bottom and times it by price=2(pi)(r^2)(price)
Next. Find the surface area of the vertical surface times by price= 2pi(r)(height)(price)
Next find height in terms of r, by using that the can must have a volume of 400pi. Since volume of a cylindar is 2pi(r)(height, then set that equal to 400pi and solve for height. Plug that into full cost equation.
C=2pi(r^2)(price of the top and bottom)+2pi(r)(height)(price of vertical surface)
Now you need to find height by using the volume given. 400pi=pi(r^2)(height)
height=400/(r^2)
C=2pi(r^2)(.02)+2pi(r)(400/(r^2))(.01)
=2pi(r^2)(.02)+2pi(400/r)(.01)
Next. Find the surface area of the vertical surface times by price= 2pi(r)(height)(price)
Next find height in terms of r, by using that the can must have a volume of 400pi. Since volume of a cylindar is 2pi(r)(height, then set that equal to 400pi and solve for height. Plug that into full cost equation.
C=2pi(r^2)(price of the top and bottom)+2pi(r)(height)(price of vertical surface)
Now you need to find height by using the volume given. 400pi=pi(r^2)(height)
height=400/(r^2)
C=2pi(r^2)(.02)+2pi(r)(400/(r^2))(.01)
=2pi(r^2)(.02)+2pi(400/r)(.01)
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Let r = radius of the cylinder in cm
and h = its height in cm
Volume, V = π r^2 h
=> h = V / (π r^2) = 400π / (πr^2) = 400/r^2 cm ... ( 1 )
Cost, C
= cost of the top and bottom + cost of the lateral surface
= 2 * π r^2 * (0.02) + 2π r h * (0.01)
Plugging the value of h from ( 1 ),
C = (0.04) π r^2 + (0.02) π r * (400/r^2)
=> C = π [ (0.04) r^2 + 8/r^2 ].
and h = its height in cm
Volume, V = π r^2 h
=> h = V / (π r^2) = 400π / (πr^2) = 400/r^2 cm ... ( 1 )
Cost, C
= cost of the top and bottom + cost of the lateral surface
= 2 * π r^2 * (0.02) + 2π r h * (0.01)
Plugging the value of h from ( 1 ),
C = (0.04) π r^2 + (0.02) π r * (400/r^2)
=> C = π [ (0.04) r^2 + 8/r^2 ].