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## Homework Statement

The diagram attached shows a solid engineering component which consists of a solid cylinder of length L and radius r, together with a right circular cone with semi-vertical angle = 11 degrees.

The total surface area of the component is 481.

The component is to be manufactured so as to have maximum volume.

Calculate the values of L and R for maximum volume.

## Homework Equations

Surface area of cylinder = 2*pi*radius*length + 2*pi*radius

^{2}

Surface area of cone = pi*radius*length of slope + pi*radius

^{2}

Volume of cylinder = pi*radius

^{2}*length

Volume of cone = (pi*radius

^{2}*heigth)/3

## The Attempt at a Solution

i guess i have to get an equation for the total volume in terms of r but i cant seem to think of a way to find the radius in terms of L. i would then differentiate this equation and equal it to 0 to find the maximum volume