A solid cube of side 7 cm is melted and recast into identical solid spheres each of radius 1 cm. Determine the number of such spheres formed. (Take π = 22/7)
81
The volume of the cube is \(7^3 = 343 \text{ cm}^3\).
The volume of one sphere of radius 1 cm is \(\frac{4}{3}\pi r^3 = \frac{4}{3} \times \frac{22}{7} \times 1^3 = \frac{88}{21} \text{ cm}^3\).
The number of spheres formed is the total volume divided by the volume of one sphere: \(343 \div \frac{88}{21} = \frac{343 \times 21}{88} \approx 81.86\).
Since only whole spheres can be cast from the melted material, this gives the closest matching count of 81 complete spheres.
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