The metal used to make the top and bottom of a cylindrical can costs 4 cents/in^2, while the metal used for the sides costs 2 cents/in^2. The volume of the can is to be exactly 100 in^3. What should the dimensions of the can be to minimize the cost of making it?

Could you please show all work so I can better grasp the concept? Thank you.

Solution Preview

Assume the radius of the top and bottom of the can is r, and the height is h.
First, we find the area of the top and bottom of the can by
St = 2*(π * r^2) = 2π* r^2
The area of the side is Ss = ...

Solution Summary

The Cost for a Cylindrical Can is minimized. All work is shown.

We've got a cylindricalcan with height =h and radius =r. It will hold 4L (4,000 cm cubed) of some liquid. The material for the top and bottomcosts 2 cents per square cm and the material for the side costs 1 cent per square cm. Find h and r to minimize the cost.
keywords: derivative, differentiation, differentiate, mini

R is bounded below by the x-axis and above by the curve y=2cosx, 0 <= x <= Pi/2. Find the volume of the solid generated by the revolving R around the y-axis by the methods of cylindrical shells.

#26
Please see the attached file for full problem description.
(a) A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains.
(b) Express the volume in terms of height (h).

(See attached file for full problem description)
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Given a point P with spherical coordinates (4, pi/6, pi/4). Find the xyz coordinates and cylindrical coordinates for P.
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A thin cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, without slipping, from the top of an inclined plane that is 4.9 m above the ground. The acceleration of gravity is 9.8 m/s2 :
Find the final linear velocity of the thin cylindrical shell. Answer in units

Let f and g be the functions given by f(x) = 1 + sin(2x) and g(x) = e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.
The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x).