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SSC MTS 2021 · PYQ · Mensuration · medium

If the total surface area of a sphere of radius r cm is equal to the total surface area of a cube of side 5 cm, which of the following is true?

  1. A.r < s✓ Correct
  2. B.r = s
  3. C.r > s
  4. D.r ≥ s

Explanation

Setting 4πr² = 6s² gives r² = 3s²/(2π). With s=5, r=√3 ≈ 1.73, whereas s=5. Since √3 < √6.28 < 5, we get r < s.
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