A cylindrical container is designed to carry liquid that must be insulated (see diagram). The interior...

   

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A cylindrical container is designed to carry liquid that must be insulated (see diagram). The interior cylinder will hold the liquid, and the insulation must be 2 inches thick. a. If the radius of the entire container (interior cylinder and insulation) is 4.5 inches, what is the radius of the interior cylinder? What if the radius of the entire container is 5.9 inches? x inches? b. The formula for the volume of a cylinder is given by V=r³h. Suppose the container must hold exactly 200 in' of liquid. How tall must the container be if the radius of the entire container is 4.5 inches and the interior cylinder holds exactly 200 in? What if the radius of the entire container is 5.9 inches? INSULATION Interior Cylinder c. Define a function /whose input x is the radius of the entire package (in inches) and whose output h is the height of the package (in inches) necessary so that the interior container holds 200 in³ of liquid. d. What happens to the value of h as x→2'? What does this mean in the context of this problem? A cylindrical container is designed to carry liquid that must be insulated (see diagram). The interior cylinder will hold the liquid, and the insulation must be 2 inches thick. a. If the radius of the entire container (interior cylinder and insulation) is 4.5 inches, what is the radius of the interior cylinder? What if the radius of the entire container is 5.9 inches? x inches? b. The formula for the volume of a cylinder is given by V=r³h. Suppose the container must hold exactly 200 in' of liquid. How tall must the container be if the radius of the entire container is 4.5 inches and the interior cylinder holds exactly 200 in? What if the radius of the entire container is 5.9 inches? INSULATION Interior Cylinder c. Define a function /whose input x is the radius of the entire package (in inches) and whose output h is the height of the package (in inches) necessary so that the interior container holds 200 in³ of liquid. d. What happens to the value of h as x→2'? What does this mean in the context of this problem?