A spherical wooden ball of radius r is to be divided into eight identical parts by cutting by planes passing through the same diameter. What is the surface area of each final piece?

  1. A. \frac{\pi r^{2}}{3}
  2. B. \frac{3\pi r^{2}}{2} ✓
  3. C. \frac{2\pi r^{2}}{3}
  4. D. \frac{4\pi r^{2}}{3}

Correct Answer: B. \frac{3\pi r^{2}}{2}

Explanation

Slicing a sphere into 8 identical wedges gives each wedge a spherical surface of \frac{1}{8} \times 4\pi r^2 = \frac{\pi r^2}{2}. The two flat semicircular faces add 2 \times \frac{\pi r^2}{2} = \pi r^2. Total surface area is \frac{\pi r^2}{2} + \pi r^2 = \frac{3\pi r^2}{2}.

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