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- Apr 22nd 2009, 12:44 PMzaurmCircular cylinder area.
- Apr 22nd 2009, 02:46 PMskeeter
assuming "largest" is in terms of volume ...

sketch the circle $\displaystyle x^2 + y^2 = 2^2$

inscribe a rectangle in the circle ... rotation of the figure about the y-axis yields a cylinder inscribed in a sphere of radius 2.

volume of a cylinder, $\displaystyle V = \pi r^2 h$

$\displaystyle V = \pi x^2 \cdot 2y = \pi x^2 \cdot 2\sqrt{4 - x^2}$

find $\displaystyle \frac{dV}{dx}$ and find the values of x and y that maximize the volume ... then determine the surface area,

$\displaystyle A = 2\pi r^2 + 2\pi rh = 2\pi x^2 + 2\pi r (2y)$