Mathematics, 21.07.2019 21:50 evan1v1123
Awedge is cut out of a circular cylinder of radius 10 by two planes. one plane is perpendicular to the axis of the cylinder. the other intersects the first at an angle of 30° along a diameter of the cylinder. find the volume v of the wedge, taking rectangular cross-sections to be parallel to the line of intersection of the two planes, which is the x-axis. (let r = 10.)
Answers: 1
![V= \int\limits^{10}_{-10} {A(x)} \, dx \\ \\ = \int\limits^{10}_{-10} {\frac{100-x^2}{2\sqrt{3}}} \, dx =2\int\limits^{10}_{0} {\frac{100-x^2}{2\sqrt{3}}} \, dx \\ \\ =\int\limits^{10}_{0} {\frac{100-x^2}{\sqrt{3}}} \, dx=\frac{1}{\sqrt{3}}\left[100x-\frac{x^3}{3}\right]^{10}_0 \\ \\ =\frac{1}{\sqrt{3}}\left[100(10)-\frac{(10)^3}{3}\right]=\frac{1}{\sqrt{3}}\left[1000-\frac{1000}{3}\right] \\ \\ =\frac{1}{\sqrt{3}}\left[\frac{2000}{3}\right]=\frac{2000}{3\sqrt{3}}](/tpl/images/0117/0903/138f3.png)
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Awedge is cut out of a circular cylinder of radius 10 by two planes. one plane is perpendicular to t...
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