A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. What is its volume?( $π$ = 3.14)

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{345.5 c m}^{3}

{346.5 cm}^{3}

{347.5 cm}^{3}

{348.5 cm}^{3}

answer is B.

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Detailed Solution

Given,
Radius of cylinder = 1 cm, height of cylinder = 8 cm, radius of sphere = 8.5 cm.
Volume of cylinder

= π r^{2} h

\Rightarrow π \times 1^{2} \times 8

\Rightarrow 8 πc m^{3}

Volume of sphere

= \frac{4}{3} π r^{3}

\Rightarrow \frac{4}{3} π \times (\frac{8.5}{2})^{3}

\Rightarrow \frac{614125}{6000} πc m^{3}

Total Volume

= (\frac{614125}{6000} + 8) π

\Rightarrow (\frac{614125 + 48000}{6000}) π

\Rightarrow \frac{662125}{6000} π

\Rightarrow 110.35 \times 3.41

\Rightarrow {346.5 cm}^{3}

Therefore, volume

= {346.5 cm}^{3}

.
Hence, the correct option is 2.

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