The curved surface area of a solid metallic right circular cylinder is 1792π cm² and its base radius is 32 cm. It is melted and recast into 42 solid spherical balls of equal radius. What is the surface area (in cm²) of a ball ?

Correct option is D

​$$\textbf{Given:} \\\text{Curved surface area of cylinder} = 1792\pi \text{ cm}^2 \\\text{Radius of cylinder} = 32 \text{ cm} \\\text{Number of spherical balls} = 42 \\\textbf{Concept Used:} \\\text{Surface area and volume conservation} \\\textbf{Formula Used:} \\\text{CSA of cylinder} = 2\pi r h \\\text{Volume of cylinder} = \pi r^2 h \\\text{Volume of sphere} = \frac{4}{3}\pi R^3 \\\text{Surface area of sphere} = 4\pi R^2 \\\textbf{Solution:} \\2\pi r h = 1792\pi \\2 \times 32 \times h = 1792 \\64h = 1792 \\h = 28 \\\text{Volume of cylinder} = \pi \times 32^2 \times 28 \\= \pi \times 1024 \times 28 \\= 28672\pi \\\text{Volume of one sphere} = \frac{28672\pi}{42} \\= \frac{2048}{3}\pi \\\frac{4}{3}\pi R^3 = \frac{2048}{3}\pi \\R^3 = 512 \\R = 8 \\\text{Surface area of one sphere} = 4\pi R^2 \\= 4\pi \times 64 \\= 256\pi \\\textbf{Final Answer:} \\256\pi$$​​