Discussion

The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is

Answer: A

Melting conserves volume, so divide the cylinder's volume by one coin's.

\[ V_{\text{coin}} = \pi (0.75)^{2}(0.2) = \pi (0.5625)(0.2) = 0.1125\pi \text{ cm}^{3} \]

\[ V_{\text{cylinder}} = \pi (3)^{2}(8) = 72\pi \text{ cm}^{3} \]

\[ n = \frac{72\pi}{0.1125\pi} = \frac{72}{0.1125} = 640 \]

The \( \pi \) cancels, so no approximation is needed anywhere in the calculation.

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