Construct a rational function that will help solve the probl

Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

A right circular cylinder is to have a volume of 55 cubic inches. It costs 4¢/square inch to construct the top and bottom and 1¢/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let x = radius. (Round your answer to two decimal places.)

____________________ in.

Solution

volume of right circular cylinder is given by V = pir^2 h

x is the radius

V = pi^ x^2 h

55 = pix^2 h

cost of constructing top of cylinder = 4 pi*x^2

cost of constructing bottom = 4* pi x^2

cost of constructing rest of the cylinder = 2*pi*x * h

so we have

55 = 8pi*x^2 + 2pi* x* h

since h = 55 / pi*x^2

function becomes

c(x) = 8pi x^2 + 2pi * x * (55/ pi * x^2 )

c(x) = 8pi x^2 + 110 / x

rational function is

C(x) = 8pi* x^3 + 110 / x

minimum cost occurs at x = 1.30 in