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September 2, 2015

Homework Help: Calculus I

Posted by Ken on Monday, November 12, 2012 at 1:11am.

*Optimization problem* [I don't know how to get to the answer] Problem: You have a cylindrical can with radius 4cm and height 10cm. Inside is a marble with a radius that has to be larger than 0 but less than 4 cm (even the largest marble will fit entirely). You're filling it with water and you stop when the height of water reaches the top of the marble. find the radius of the marble requiring the most water to cover it. Hint: Volume of water in a cylinder with radius R and height of water H is given by V=PiR^2^H and volume of a sphere with radius r is given by V=4/3Pi(r^3^). Consider: if the water is just covering the marble of radius r, what is the height of the water in the can?

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