You plan to build a cylindrical container with no top. The material used for the lateral sides costs $6 per square foot while the material for the bottom costs $9 per square foot. (a) Express the surface area of the open cylinder in terms of the cylinder's radius, r, and height, h. S = (b) Express the cost of building the open cylinder in terms of the cylinder's radius, r, and height, h. C = (c) If the volume of the cylindrical container is 500 cubic feet, express the cost of building the cylinder, C in terms of the cylinder's radius, r. C (r) = (d) If the volume of the cylindrical container is V cubic feet, express the cost of building the cylinder, C in terms of the cylinder's radius, r. Note - Your answer will have V in it, but V is a constant here. Use an upper case V. C (r) =

Question

Mathematics

Peters

6 December, 14:42

You plan to build a cylindrical container with no top. The material used for the lateral sides costs $6 per square foot while the material for the bottom costs $9 per square foot. (a) Express the surface area of the open cylinder in terms of the cylinder's radius, r, and height, h. S = (b) Express the cost of building the open cylinder in terms of the cylinder's radius, r, and height, h. C = (c) If the volume of the cylindrical container is 500 cubic feet, express the cost of building the cylinder, C in terms of the cylinder's radius, r. C (r) = (d) If the volume of the cylindrical container is V cubic feet, express the cost of building the cylinder, C in terms of the cylinder's radius, r. Note - Your answer will have V in it, but V is a constant here. Use an upper case V. C (r) =

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Answers (1)

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Dinosaur · Answer 1

Step-by-step explanation:

Since open cylinder surface area includes only bottom area and curved SA

a) Surface area of the given cylinder

= curl surface area + bottom surface area

S = 2pir h + pir^2

b) Cost C = 2pir h (6) + 9 (pir^2) = 12 pirh + 9 pir^2

c) V = pir^2 h=500

Hence h = 500/pir^2

C (r) = 12 pirh + 9 pir^2

= 12 / 500r + 9 pir^2

d) If V is constant and unknown

then h = V/pir^2

Hence C (r) = 12 / Vr + 9 pir^2