Discussion
A cylinder having radius 1 m and height 5 m, is completely filled with wine. In how many conical flasks can this wine be filled into if the flask radius and height is 50 cm each?
Answer: C
Work in centimetres throughout: the cylinder is \( r = 100 \) cm, \( h = 500 \) cm.
\[ V_{\text{cyl}} = \pi (100)^{2}(500) = 5{,}000{,}000\pi \text{ cm}^{3} \]
\[ V_{\text{cone}} = \frac{1}{3}\pi (50)^{2}(50) = \frac{125000\pi}{3} \text{ cm}^{3} \]
\[ n = \frac{5{,}000{,}000\pi}{125000\pi/3} = \frac{5{,}000{,}000 \times 3}{125000} = 120 \]
Mixing metres and centimetres is the trap here - the units must be made consistent before any division.
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