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JAMB 1986 · UME · Q36

A solid prism has the trapezium PQRSPQRS as its uniform cross-section, with parallel vertical sides PQ=6PQ = 6 m and SR=11SR = 11 m, QR=12QR = 12 m perpendicular to both, and length 8 m. Find its volume.

Worked solution (try it first)
  1. The cross-section is a trapezium with parallel sides 6 m and 11 m, 12 m apart.
  2. Its area is half the sum of the parallel sides times the distance between them: 12(6+11)×12=102 m2\frac12(6 + 11) \times 12 = 102\text{ m}^2.
  3. Volume of a prism = cross-section area × length: 102×8=816 m3102 \times 8 = 816\text{ m}^3, option C.

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