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A godown has vertical walls enclosing a space 18 m long, 10 m wide and 4 m high, and above the walls sits a roof whose cross-section is a triangle spanning the full 10 m width and rising 3 m to the ridge. The roof runs the whole 18 m length. How much space, in cubic metres, does the godown enclose altogether?

Competition practiceMensuration
  • A990
  • B720
  • C1260
  • D900

Step-by-Step Solution

Treat the building as two stacked prisms sharing the same 18 m length. The lower part is a cuboid: 4 = 720 cubic m. The roof is a triangular prism whose cross-section measures sq m, so it holds cubic m. Together 720 + 270 = 990 cubic m. The trap 720 stops at the walls and forgets the roof space entirely; 1260 counts the roof as a cuboid 18 = 540 and drops the 1/2 from the triangle; 900 applies a pyramid's 1/3 to that 540, but a roof of constant cross-section is a prism, not a pyramid, so no 1/3 belongs there.
Answer: A) 990

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