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recoil33
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Q. You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 130 cm3, what values of h and r will minimise the total surface area (including the top and bottom faces)?
Volume(Cylinder) = pi(r)2*h
130 = pi(r)2*h
Surface Area(Cylinder) = 2pi(r)*h
______________________________________
Because I'm working with 2 variales, r and h I'm a bit confused. Let alone, working with the two equations (Surface Area & Volume).
Firstly, changing h in the form of r.
h = 130/pi(r)2
therefore:
130 = pi(r)2*(130/pi(r)2)
Now, i should differentiate this.
0 = 2pi(r) * (0*(pi(r)2) - (130*2pi(r)) / ((pi(r)2)2)
I'm a bit confused as of what to do now, I've just finished previous optimisation questions although nothing with a cylinder like this.
Any help would be appreciated, thank you.
Volume(Cylinder) = pi(r)2*h
130 = pi(r)2*h
Surface Area(Cylinder) = 2pi(r)*h
______________________________________
Because I'm working with 2 variales, r and h I'm a bit confused. Let alone, working with the two equations (Surface Area & Volume).
Firstly, changing h in the form of r.
h = 130/pi(r)2
therefore:
130 = pi(r)2*(130/pi(r)2)
Now, i should differentiate this.
0 = 2pi(r) * (0*(pi(r)2) - (130*2pi(r)) / ((pi(r)2)2)
I'm a bit confused as of what to do now, I've just finished previous optimisation questions although nothing with a cylinder like this.
Any help would be appreciated, thank you.
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