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Find the volume enclosed by the spheres x2 + y2 + z2 = a2 and x2 + y2 + z2 = b2 where b > a. |
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Answer» Radius of sphere x2 + y2 + z2 = b2 is b and radius x2 + y2 + z2 = a2 is a(b > a) Enclosed volume = volume of sphere x2 + y2 + z2 = b2 - volume of sphere x2 + y2 + z2 = a2 = \(\frac43\pi b^3-\frac43\pi a^3\) (\(\because\) volume of sphere of radius r = \(\frac43\pi r^3\)) = \(\frac43\pi(b^3-a^3)\) = \(\frac43\pi(b-a)(b^2+a^2+ab)\) cubic units. |
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