the height of a right cylinder is 6r, where r is the radius. Write a function f in simplest form that represents the ratio of the surface area to the volume

ratio of surface area to volume = 7 to ratio 3r

Step-by-step explanation:

The volume of a cylinder = πr²h

Surface area = 2πr (r + h)

where

r = radius

h = height

h = 6r

where

r = radius

volume = πr²h

volume = π * r² * 6r

volume = 6πr³

surface area = 2πr (r + h)

surface area = 2 * π * r (r + 6r)

surface area = 2πr (7r)

surface area = 14πr²

surface area = 14πr²

ratio of surface area to volume = 14πr² / 6πr³

ratio of surface area to volume = 7/3r

ratio of surface area to volume = 7 to ratio 3r

7/3r

Step-by-step explanation:

To find the simplest form, we must find the relationship between the surface area and volume of a cylinder. The cylinder with radius r and height h has;

surface area = 2πr (r + h)

volume = πr²h

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

= 2 (r + 6r) : r (6r)

= 14r : 6r²

= 7:3r