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JAMB Mathematics 1978 Question 35

Question 35

Mensuration of Solids

A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cylinder of radius 3cm and height 4cm. Which of the following statements is true?

  1. A.The volume of the sphere is greater than the volume of the cone.
  2. B.The volume of the cone is less than the volume of the cylinder
  3. C.The total surface area of the cone is greater than that of the sphere
  4. D.The total surface area of the cylinder is less than that of the sphere
  5. E.The total surface area of the cone is equal to that of the cylinder.
Show the answer and explanation

Answer: C (The total surface area of the cone is greater than that of the sphere)

Explanation

All three volumes equal 36π, so A and B are false. Surface areas: sphere 36π, cylinder 2π(3)(4) + 18π = 42π, cone π(3)(√153) + 9π ≈ 46π. Only C is true.