Question

Drink in a cylindrical can with height h and radius r, A) If the volume of the can is 87.5pi, state h in terms of r? B) Obtain the total surface area of the can in terms of r? C) Calculate the radius of the cylinder if the total surface area is minimum?

Answer 1

`r=3.52`

Explanation:

`V=pir^2h`

`87.5pi=pir^2h`

`(87.5pi)/(pir^2)=h`

`87.5/r^2=h`

`2pir^2+2pirh=SA`

Substitute for `h`:

`2pir^2+2pir(87.5/r^2)=SA`

`2pir^2+(175pi)/r= SA`

graph{2pix^2+(175pi)/x [-45.7, 64.47, 222.62, 277.7]}

Graph the equation and look for when y is minimum but x still has to be positive