The height of a right cylinder is 2r, where r is the radius. Write a function f in simplest form that represents the ratio of the surface area to the volume.

Question

Not sure how to do this without the area?

Answer 1

The surface area of a right cylinder is the area of the top circle (pi*r^2), the area of the bottom circle (pi*r^2), and the area of the curved-around side (2*pi*r*h).   

 

The volume of a right cylinder is pi*r^2*h.

 

Since h = 2r, 

 

Surface area becomes pi*r^2 + pi*r^2 + 2*pi*r*(2r)  <--- this (2r) = h

 

or  Surface area = 2(pi*r^2) + (4*pi*r^2)= 6 pi r^2

 

Volume (using h=2r) = pi*r^2(2r) = 2 pi r^3

 

 

 

The ratio of these is:

 

6 pi r^2

----------

2 pi r^3

 

 

6 

-- = 3  

2          

 

pi

--- = 1

pi

 

r^2            1

----- = --------

r^3            r

 

Putting all of this together,

 

Surface Area             3

--------------- = --------------------

    Volume                 r