Consider the equation x + y + (Rz/H) = R. If we have two solids with...

     
 
 
 
 
 

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Consider the equation x² + y² + (Rz/H)² = R². If we have two solids with the same radius R and height H, one with density d(x, y, z) = 1 and the other with density 8(x, y, z) = 2√x² + y², which values of R, H will ensure that they both have the same mass? The answer to this question will be a relation involving R, H. For which values of R, H will the second solid have bigger mass? Choose positive values for R, H, so that the two solids have the same mass. Plot the body with the centroid in red. Consider the equation x² + y² + (Rz/H)² = R². If we have two solids with the same radius R and height H, one with density d(x, y, z) = 1 and the other with density 8(x, y, z) = 2√x² + y², which values of R, H will ensure that they both have the same mass? The answer to this question will be a relation involving R, H. For which values of R, H will the second solid have bigger mass? Choose positive values for R, H, so that the two solids have the same mass. Plot the body with the centroid in red.

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