Discussion
If circular metal sheet is 0.65cm thick and of 50cm in diameter is melted and recast into cylindrical bar with 8cm diameter then length of bar will be
Answer: A
Melting conserves volume, so equate the sheet's volume with the bar's.
\[ V_{\text{sheet}} = \pi (25)^{2}(0.65) = \pi (625)(0.65) = 406.25\pi \text{ cm}^{3} \]
\[ V_{\text{bar}} = \pi (4)^{2} L = 16\pi L \]
\[ 16\pi L = 406.25\pi \quad\Longrightarrow\quad L = \frac{406.25}{16} = 25.39 \text{ cm} \]
The \( \pi \) cancels, so no value for it is needed. Both diameters must be halved first - using 50 and 8 directly would give the same ratio, but the thickness would then be mismatched.
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