Question 118

A rectangular examination hall having seats for 500 candidates has to be built so, as to allow 4 cubic metres of air and 0.5 square metres of floor area per candidate. If the length of hall be 25m, find the height and breadth of the hall.

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Solution

Total number of seats in rectangular examination hall = 500
Length of the hall = 25 m
Cubic metres of air per candidate $= 4 m^{3}$
Square metres of floor area per candidate $= 0.5 m^{2}$
$∴$ Height of the hall $= \frac{V o l u m e o f a i r p e r c a n d i d a t e}{S q u a r e m e t r e o f f l o o r a r e a f o r o n e c a n d i d a t e} = \frac{4}{0.5} = \frac{40}{5} = 8 m$

Total capacity of the hall $= N o . o f c a n d i d a t e s \times a i r c a p a c i t y p e r c a n d i d a t e$
$= 500 \times 4 = 2000 m^{3}$

$∴$ Breadth of the hall $= \frac{2000}{25 \times 8} = \frac{80}{8} = 10 m$

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