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A spherical glass vessel has a cylindrical neck $7$ cm long and $8$ cm in diameter. The radius of spherical part is $10$ cm. Find the volume of the vessel.
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Solution: (a) Volume of the vessel $= \frac{4}{3} \times \frac{22}{7} \times 10 \times 10 \times 10 + \frac{22}{7} \times 4 \times 4 \times 7 = 4190.4 + 352 = 4542.48$ cu. cm