Question

Consider a cylinder with height h=3x-4 and radius r=3x+2 Determine a simplified expression for the ratio of the volume of the cylinder to its surface area. Make a sketch of the cylinder

Answer 1

Explanation:

Given that,

The height of the cylinder, h = 3x-4

The radius of the cylinder, r = 3x+2

The volume of the cylinder is :

`V=\pi r^2 h`

The surface area of the cylinder is :

`A=2\pi r(r+h)`

The ratio of the volume of the cylinder to the surface area of the cylinder is :

`(V)/(A)=(\pi r^2h)/(2\pi r(r+h))\\\\(V)/(A)=(rh)/(2(r+h))`

Put all the values,

`(V)/(A)=((3x+2)(3x-4))/(2(3x+2+3x-4))\\\\(V)/(A)=((3x+2)(3x-4))/(2(6x-2))`

Hence, this is the required solution.