A cylindrical iron rod of radius $7$ cm and length $20$ cm is melted and recast into a cube. The edge of the…
A cylindrical iron rod of radius $7$ cm and length $20$ cm is melted and recast into a cube. The edge of the cube formed is (use $\pi=\dfrac{22}{7}$):
$22$ cm
$11$ cm
$14$ cm
$7$ cm
Solution
Volume of rod $= \pi r^{2} h = \dfrac{22}{7} \times 49 \times 20 = 22 \times 7 \times 20 = 3080 \text{ cm}^{3}$. Hmm, $\sqrt[3]{3080} \approx 14.55$, not a clean integer. Re-reading the problem: with $r=7, h=20$ the cube edge is approximately $14.55$ cm. Among the given choices the closest is $14$ cm (assuming the question intends a near-cube approximation). Strict computation: $a = \sqrt[3]{3080} \approx 14.55$, so option (c) $14$ cm is the best integer match.