A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 4¢per square centimeter, while the sides are made of material that costs 2¢per square centimeter.
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs
![(a) Express the total cost C of the material as a function of the radius r of the cylinder. Find the right side of the equation. Express the cost in dollars.
C(r) =
(Simplify. Type an exact answer in terms of T.)
(b) Graph C= C(r) using your graphing utility. Which graph shown below i
the graph of C(r), as displayed on a graphing utility? All four graphs use the following limits: [0, 10] by [0, 35], Xscl = 1, Yscl = 4.
O A.
O B.
Oc.
O D.
For what value of r is the cost C a minimum?
r=
centimeters (Round your answer to two decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7362fbb-c143-400b-8ee4-1fef2b2882aa%2F512355c2-33bb-4769-acb1-2e4ac146be0b%2Ffv9o5p_processed.png&w=3840&q=75)
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