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A spherical glass vessel has a cylindrical neck which is $7 \text{ cm}$ long and $2 \text{ cm}$ in diameter. The diameter of the spherical part is $14 \text{ cm}$. Find the capacity of the entire glass vessel. (Use $\pi = \frac{22}{7}$)
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Solution: Radius of sphere $= R = 7 \text{ cm}$
Radius of cylinder $= r = 1 \text{ cm}$
Capacity of the entire glass vessel $= \pi r^2 h + \frac{4}{3} \pi R^3$ [2+2 marks]
$= \frac{22}{7} \times 1 \times 1 \times 7 + \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$
$= \frac{4378}{3} \text{ cu.cm}$ or $1459.33 \text{ cu.cm}$ [1 mark]
Radius of cylinder $= r = 1 \text{ cm}$
Capacity of the entire glass vessel $= \pi r^2 h + \frac{4}{3} \pi R^3$ [2+2 marks]
$= \frac{22}{7} \times 1 \times 1 \times 7 + \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$
$= \frac{4378}{3} \text{ cu.cm}$ or $1459.33 \text{ cu.cm}$ [1 mark]