Mathematics: 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

Add 25 to both sides to isolate the variable xso the answer would be:x=38...

Consider a cylinder with height h=3x-4 and radius

unknownyobutt21

21.06.2021

Step-by-step 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 :

$\dfrac{V}{A}=\dfrac{\pi r^2h}{2\pi r(r+h)}\\\\\dfrac{V}{A}=\dfrac{rh}{2(r+h)}$

Put all the values,

$\dfrac{V}{A}=\dfrac{(3x+2)(3x-4)}{2(3x+2+3x-4)}\\\\\dfrac{V}{A}=\dfrac{(3x+2)(3x-4)}{2(6x-2)}$

Hence, this is the required solution.

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