Mathematics, 24.09.2019 12:00 jesser9
Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 = 9 and the sphere x2 y2 z2 = 16.
Answers: 1
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![\int\limits^{\sqrt{16-r^2} }_0 r \ dz = [rz]^{\sqrt{16-r^2} }_0](/tpl/images/0258/0642/74ae4.png)
![\int\limits^3_0 r\sqrt{16-r^2} \ dr = [-\frac{1}{3}(16-r^2)^{\frac{3}{2} } ]^3_0](/tpl/images/0258/0642/249d6.png)
![\int\limits^{2x}_0 {\frac{64-7\sqrt{7} }{3} } \ d\Theta = [(\frac{64-7\sqrt{7} }{3} )\Theta]^{2x}_0](/tpl/images/0258/0642/e147e.png)
, 
, and 
. Converting to cylindrical coordinates, using
, and the region is given in cylindrical coordinates by 
, 
, and 
.
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Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 =...
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