A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.7 times as much as the concrete (per unit of surface area). If the volume of the silo is 650 m³, what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome. What is the function of the cost of the silo, C, in terms of the radius, r? 650 2 C= 2xr +3.4mr² (Type an expression. Type an exact answer, using as needed.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation. Round to the nearest tenth as needed.)
A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.7 times as much as the concrete (per unit of surface area). If the volume of the silo is 650 m³, what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome. What is the function of the cost of the silo, C, in terms of the radius, r? 650 2 C= 2xr +3.4mr² (Type an expression. Type an exact answer, using as needed.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation. Round to the nearest tenth as needed.)
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.7 times as much
as the concrete (per unit of surface area). If the volume of the silo is 650 m³, what are the dimensions of the silo (radius and height of the
cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome.
What is the function of the cost of the silo, C, in terms of the radius, r?
(650 2
+3.4Rr²
²3
(Type an expression. Type an exact answer, using a as needed.)
C= 2xr
The interval of interest of the objective function is.
(Simplify your answer. Type your answer in interval notation. Round to the nearest tenth as needed.)
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