Discussion
A hall is 15 m long and 12 m broad. If the sum of areas of the floor and ceiling is equal to the sum of areas of four walls, the volume of the hall is in m3 is:
Answer: B
The volume is 1200 m3.
Floor plus ceiling is \(2lb\); the four walls are \(2h(l + b)\). Setting them equal:
\[ \begin{aligned} 2 \times 15 \times 12 &= 2h(15 + 12) \\ 360 &= 54h \\ h &= \tfrac{20}{3}\ \text{m} \\ V &= 15 \times 12 \times \tfrac{20}{3} = 1200\ \text{m}^{3} \end{aligned} \]
720 m3 comes from a height of 4 m and 900 m3 from 5 m; both ignore the condition. 840 m3 does not correspond to any height that satisfies it.
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