Discussion
The number of coins, 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is
Answer: C
Melting conserves volume, so divide the target cylinder's volume by one coin's. Halve both diameters first.
\[ V_{\text{coin}} = \pi (0.75)^{2}(0.2) = 0.1125\pi \text{ cm}^{3} \]
\[ V_{\text{cylinder}} = \pi (2.25)^{2}(10) = 50.625\pi \text{ cm}^{3} \]
\[ n = \frac{50.625\pi}{0.1125\pi} = \frac{50.625}{0.1125} = 450 \]
Using the diameters directly instead of the radii leaves the ratio unchanged only because both are squared - but the thickness is not, so it is safer to convert first.
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