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A perfume bottle is in the form of a cylinder but the bottom of the bottle has a hemispherical raised portion to reduce the capacity of the bottle. The inner diameter of the bottle is $5$ cm and the height of the bottle is $10$ cm. Find the capacity of the perfume bottle in mL. (Use $\pi = 3.14$ and $1 \text{ cm}^3 = 1 \text{ mL}$)
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Radius $r = \frac{5}{2}$ cm, $h = 10$ cm. Volume $= \pi r^2 h - \frac{2}{3} \pi r^3 = 3.14 \times \frac{5}{2} \times \frac{5}{2} \times 10 - \frac{2}{3} \times 3.14 \times \left(\frac{5}{2}\right)^3 = \frac{3925}{24} \approx 163.5$ cu. cm. Capacity $= 163.5$ mL. ($\frac{1}{2} + 1\frac{1}{2} + 1\frac{1}{2} + 1 + \frac{1}{2}$ marks)