Answer to Question #109950 in Geometry for Sara Ahmad

Question

A packaging plant quality assurance agent compares the surface area and volume of packages to ensure the packages will be transported economically. The most popular package size is a cylinder with a height of 18 inches. Write and simplify an expression that represents the ratio of the surface area to the volume of the cylinder.

Answer 1

Solution.

Volume of cylinder:

V = πR²h, as h = 18 inches, V = πR² ∙ 18

Surface area:

S = 2πR∙(h+R), as h = 18 inches: S = 2πR∙(h+18)

Thus, the ratio of the surface area to volume of the cylinder is:  S/V =( 2πR ∙(18+R))/ (πR²∙ 18) = (2 ∙(18+R))/(18∙R) =(18+R)/(9∙R)

Answer:  S/V = (18+R)/(9∙R) .