Mathematics, 29.11.2020 15:00 hectorgonzalejr333
Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along a diameter at an angle of π/6
Answers: 1
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![=\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}](/tpl/images/0932/3613/58090.png)
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Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along...
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