CDS 2026 (I) Elementary Mathematics, question 58

Topic: Mensuration

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Q58

A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise ?

  1. (a) 73\frac{7}{3} cmCorrect answer
  2. (b) 83\frac{8}{3} cm
  3. (c) 143\frac{14}{3} cm
  4. (d) 163\frac{16}{3} cm

Solution.

Answer: (a) 73\frac{7}{3} cm

  1. A fully submerged sphere displaces its own volume.
  2. If the water rise is h, then π(14)2h=(4/3)π(7)3\pi(14)^{2}h = (4/3)\pi(7)^{3}.
  3. Cancel π\pi and simplify to h=7/3cmh = 7/3cm, assuming no overflow.