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Find the volume of the described solid S: the base of S is a circular disk with radius r. Parallel crosssections perpendicular to the base are squares.
 2 years ago
 2 years ago
Find the volume of the described solid S: the base of S is a circular disk with radius r. Parallel crosssections perpendicular to the base are squares.
 2 years ago
 2 years ago

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dumbcowBest ResponseYou've already chosen the best response.1
dw:1329557645302:dw Due to symmetry we can integrate from 0 to r and just double the integral \[V = 2\int\limits_{0}^{r}A(x) dx\] \[V = 8\int\limits_{0}^{r}(r^{2}x^{2}) dx\] \[8  r^{2}x  x^{3}/3 = 8(r^{3}  r^{3}/3) = \frac{16}{3}r^{3}\]
 2 years ago
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