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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 arh+ 2/r² = ⒸS = 2πrh + ar² Os = arh+ ar² OS = 2nrh+ 2nr² OS 2nrh+ 2xr (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. ** 2V 2 + r 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. 28V 2 C(r) = (d) Find C '(r) = +5m r= 281 ✓ +10ar (e) Find the critical point of C(r). 3/ 28V 10m X X

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 arh+ 2/r² = ⒸS = 2πrh + ar² Os = arh+ ar² OS = 2nrh+ 2nr² OS 2nrh+ 2xr (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. ** 2V 2 + r 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. 28V 2 C(r) = (d) Find C '(r) = +5m r= 281 ✓ +10ar (e) Find the critical point of C(r). 3/ 28V 10m X X

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 63E
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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 O S = 2πrh + ² S = πrh + ² S = 2лrh + 2πr² S = 2πrh + 2πr O (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(r) = (d) Find C'(r) 2V 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. 28V r r = 2 +лr 2 +5πr² 28V + 10лr (e) Find the critical point of C(r). 3/ 28V 10π
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 O S = 2πrh + ² S = πrh + ² S = 2лrh + 2πr² S = 2πrh + 2πr O (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(r) = (d) Find C'(r) 2V 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. 28V r r = 2 +лr 2 +5πr² 28V + 10лr (e) Find the critical point of C(r). 3/ 28V 10π
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