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# C1 Stationary Points watch

1. I have 2 questions here:

1) Open cardboard boxes are to be made and each box must have a square base and a capacity of 4000cm3. Find the dimensions of the box which contains the minimum area of cardboard.

2) A cylinder is cut from a solid sphere of radius 3cm. Given that the cylinder has a height of 2h, find its radius in terms of h. Hence show that the volume, Vm3, of the cylinder is given by V=2πh(9-h^2). Find the max volume of the cylinder as h varies.

Thanks. It's doing my head in....
2. 1) V = 4000 = b^2.l
SA = b^2 + 4bl write all in terms of b or l, differentiate and equate to zero, find the other variable.

2) draw a side view of the sphere, and the cylinder inside it. apply pythagoras.

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Updated: October 15, 2006
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