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SSC CHSL 2025 · PYQ · Mensuration · medium

The total surface area of a cylinder is equal to its volume. Find the relation between radius and height.

Answer

The correct answer is D: h = 2r/(r-2). Total surface area = 2πr(r+h) and Volume = πr²h. Setting equal: 2πr(r+h) = πr²h → 2(r+h) = rh → 2r+2h = rh → 2r = rh-2h = h(r-2) → h = 2r/(r-2).

  1. A.h = 4r/(r-2)
  2. B.h = 3r/(r-2)
  3. C.h = r/(r-2)
  4. D.h = 2r/(r-2)✓ Correct

Explanation

Total surface area = 2πr(r+h) and Volume = πr²h. Setting equal: 2πr(r+h) = πr²h → 2(r+h) = rh → 2r+2h = rh → 2r = rh-2h = h(r-2) → h = 2r/(r-2).
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