Question

A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 2.1 times as much as the concrete​ (per unit of surface​ area). If the volume of the silo is 600m^3

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?

C=_________

​(Type an expression. Type an exact​ answer, using

piπ

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.)

The radius of the cylindrical base​ (and of the hemispherical​ dome) is

_____

mm

.

​(Round to the nearest tenth as​ needed.)

The height of the cylindrical base is

______

mm

.

​(Round to the nearest tenth as​ needed.)

Answer 1

Thank you so much sir