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What is the area of the largest sphere that can be placed inside a cube of volume 216cm³?

Answer: B) 36π\pi

  1. A) 49π\pi/3
  2. B) 36π\pi
  3. C) 152\sqrt{2}π\pi
  4. D) 32\sqrt{2}π\pi

Explanation

B) 36π\pi. The cube's side is 2163\sqrt[3]{216} = 6 cm. The largest sphere inside touches all six faces, so its diameter equals the side and r = 3 cm. Its surface area is 4π\pi r2r^2 = 4π\pi ×\times 9 = 36π\pi cm². Its volume, 43\frac{4}{3}π\pi r3r^3, also happens to be 36π\pi, so either reading gives B.

Asked in: Petrobangla 2011

Topic: Geometry and Mensuration