Question

The height of a right cylinder is 4r, where r is the radius. Write a function f in simplest form that represents the ratio of the surface area to the volume.

f(r)=

Answer 1

f(r) = 5/2r

Explanation:

To find the function f in simplest form that represents the ratio of the surface area to the volume, the relationship between the surface area and volume of a cylinder must first be established.

The cylinder with radius r and height h has a

surface area = 2πr (r + h)

and

volume = πr²h

where π is a constant

hence the ratio of surface area to volume

= 2πr (r + h) : πr²h

= 2(r + h) = rh

Hence if the height is 6r and the radius is r

The ratio is

f(r) = 2(r + 4r) : r(4r)

= 10r : 4r²

= 5:2r