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JAMB Mathematics 1982 Question 40

Question 40

Mensuration of Solids

The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are

  1. A.(21cm3, 3cm3)
  2. B.(24cm3, 3cm3)
  3. C.(24cm3, 21cm3)
  4. D.(72cm3, 3cm3)
  5. E.(63cm3, 9cm3).
Show the answer and explanation

Answer: A ((21cm3, 3cm3))

Explanation

Whole volume = ⅓ × 3² × 8 = 24cm³. The top part is a similar pyramid with half the height, so its volume is 24 × (½)³ = 3cm³, leaving 21cm³ for the bottom part.