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We want to construct a container in the shape of a cylinder. The container will have a bottom but no top. (a) Find a formula for the surface area of the container terms of the radius and height of the cylinder. Os=arh+ 2r² Os=2arh+²2 Os = arh+ ²2² OS=2arh + 2r² OS-2nrh+ 2nr (b) Suppose the container has a fixed volume V. Express the surface area of the container in terms of the radius only. Your answer will also have V in it, but that will be a parameter. Use upper case V and lower case r. You should also simplify your ar $(r) = (c) Suppose the material for the bottom costs $14 per square foot and the material for the sides costs $5 per square foot. Express the total cost in terms of the radius only. Again, your answer will also have V in it. C(r) = (d) Find C (r) - (e) Find the critical point of C(r).

We want to construct a container in the shape of a cylinder. The container will have a bottom but no top. (a) Find a formula for the surface area of the container terms of the radius and height of the cylinder. Os=arh+ 2r² Os=2arh+²2 Os = arh+ ²2² OS=2arh + 2r² OS-2nrh+ 2nr (b) Suppose the container has a fixed volume V. Express the surface area of the container in terms of the radius only. Your answer will also have V in it, but that will be a parameter. Use upper case V and lower case r. You should also simplify your ar $(r) = (c) Suppose the material for the bottom costs $14 per square foot and the material for the sides costs $5 per square foot. Express the total cost in terms of the radius only. Again, your answer will also have V in it. C(r) = (d) Find C (r) - (e) Find the critical point of C(r).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.1: Parabolas
Problem 65E
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We want to construct a container in the shape of a cylinder. The container will have a bottom but no top. (a) Find a formula for the surface area of the container in terms of the radius and height of the cylinder. Os = πrh + 2πr² S = 2πrh + ²² S = πrh + πr² Os = 2πrh + 2πr² OS = 2πrh + 2πr (b) Suppose the container has a fixed volume V. Express the surface area of the container in terms of the radius only. Your answer will also have V in it, but that will be a parameter. Use upper case V and lower case r. You should also simplify your answer. S(r) = (c) Suppose the material for the bottom costs $14 per square foot and the material for the sides costs $5 per square foot. Express the total cost in terms of the radius only. Again, your answer will also have V in it. C(r) = = (d) Find C'(r) = (e) Find the critical point of C(r). r =
Transcribed Image Text:We want to construct a container in the shape of a cylinder. The container will have a bottom but no top. (a) Find a formula for the surface area of the container in terms of the radius and height of the cylinder. Os = πrh + 2πr² S = 2πrh + ²² S = πrh + πr² Os = 2πrh + 2πr² OS = 2πrh + 2πr (b) Suppose the container has a fixed volume V. Express the surface area of the container in terms of the radius only. Your answer will also have V in it, but that will be a parameter. Use upper case V and lower case r. You should also simplify your answer. S(r) = (c) Suppose the material for the bottom costs $14 per square foot and the material for the sides costs $5 per square foot. Express the total cost in terms of the radius only. Again, your answer will also have V in it. C(r) = = (d) Find C'(r) = (e) Find the critical point of C(r). r =
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