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Total Surface Area of a Cuboid

A hollow cube...

Question

A hollow cube of side $4 c m$ contains a solid sphere touching its sides. Find the volume of gaps bet sphere & cube.

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Solution

radius of sphere $= \frac{a}{2}$
Where side of cube $= a$
Volume of gaps =volume of cube-volume of sphere $= a^{3} a^{3} - \frac{4}{3} π r^{3} = a^{3} (1 - \frac{π}{6})$

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