Consider a solid cylinder of radius R cm and height H cm (oriented like a can,...

 

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Consider a solid cylinder of radius R cm and height H cm (oriented like a can, so that the top and bottom are disks). Suppose the density of the solid at any point depends only on the height of that point; points at the bottom have density 10 g/cm, points at the top have density 4 g/cm, and the density varies linearly with height. (a) Using just your intuition, what you think the mass of the cylinder is? Explain your guess. (b) Set up and evaluate a triple integral to verify your guess, and include units in your final answer. (c) If you didn't already do so in #4(b), explain how you found the integrand and bounds in complete sentences. (Imagine you're explaining it to a friend.) Consider a solid cylinder of radius R cm and height H cm (oriented like a can, so that the top and bottom are disks). Suppose the density of the solid at any point depends only on the height of that point; points at the bottom have density 10 g/cm, points at the top have density 4 g/cm, and the density varies linearly with height. (a) Using just your intuition, what you think the mass of the cylinder is? Explain your guess. (b) Set up and evaluate a triple integral to verify your guess, and include units in your final answer. (c) If you didn't already do so in #4(b), explain how you found the integrand and bounds in complete sentences. (Imagine you're explaining it to a friend.)