Discussion
A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl?
Answer: C
The liquid's volume is conserved, so divide the bowl's by one bottle's. The bottle's radius is \( 3 \div 2 = 1.5 \) cm.
\[ V_{\text{bowl}} = \frac{2}{3}\pi (9)^{3} = \frac{2}{3}\pi (729) = 486\pi \text{ cm}^{3} \]
\[ V_{\text{bottle}} = \pi (1.5)^{2}(4) = 9\pi \text{ cm}^{3} \]
\[ n = \frac{486\pi}{9\pi} = 54 \]
A hemisphere is two thirds of \( \pi r^{3} \), not one half of the sphere formula misapplied - the \( \tfrac{2}{3} \) is what makes the count come out whole.
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