A school room is be built to accommodate 70 children so as to allow 2.2 m2 of floor and 11 m3 of space for each child. If the room be 14 metres long, what must be its breadth and height ?
Options:
A . 11 m, 4 m
B . 11 m, 5 m
C . 12 m, 5.5 m
D . 13 m, 6 m
Answer: Option B Let the breadth and height of the room be b and h metres respectively. Then, Area of the floor $$ = \left( {14b} \right)\,{m^2}$$ $$\eqalign{ & \therefore 14b = 2.2 \times 70 \cr & \Rightarrow b = \frac{{2.2 \times 70}}{{14}} \cr & \Rightarrow b = 11 \cr} $$ Volume of the room : $$\eqalign{ & = \left( {14 \times 11 \times h} \right){m^3} \cr & = \left( {154h} \right){m^3} \cr} $$ $$\eqalign{ & \therefore 154h = 11 \times 70 \cr & \Rightarrow h = \frac{{11 \times 70}}{{154}} \cr & \Rightarrow h = 5 \cr} $$
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