Q.A solid cone with a diameter of 16 cm and a height of 2 cm is melted to form 12 identical spheres. What is the diameter of each sphere? (a) \(\sqrt3\) cm (b) 2 cm (c) 3 cm (d) 4 cm
Answer: D
Let the radius of each sphere be \(r\) cm. \[ \therefore\ \text{According to the question,} \quad \frac{4}{3}\pi r^3 \times 12 = \pi \times 8^2 \times 2 \] Simplifying, \[ r^3 = \frac{128}{16} = 8 \] \[ r = 2 \] \(\therefore\) The diameter of each sphere = \(2 \times 2 = 4\) cm.
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