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 25 m, find the height and breadth of the hall.
Solution:
Total Volume of air requirement = 500 × 4 m³ = 2000m³
The total requirement space per candidate = 0.5m²
Total area requirement = 0.5 × 500 = 250 m²
Length of the hall is = 25m
The breadth of the hall = 250/25 = 10m
Now Volume of the hall required is 2000m³
Therefore the height of the hall = 2000/(25 × 10) = 8m
The height and breadth of the hall are = 8m and 10m respectively.
✦ Try This: A rectangular examination hall having seats for 1000 candidates has to be built so as to allow 4.5 cubic metres of air and 0.35 square metres of floor area per candidate. If the length of the hall is 30 m, find the height and breadth of the hall.
Total Volume of air requirement = 1000 × 4.5 m³ = 4500m³
The total requirement space per candidate = 0.45m²
Total area requirement = 0.45 × 500 = 225 m²
Length of the hall is = 30m
The breadth of the hall = 225/30 = 7.5 m
Now Volume of the hall required is 4500 m³
Therefore the height of the hall = 4500/(30 × 7.5) = 20m
The height and breadth of the hall are = 7.5m and 20m respectively.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 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 25 m, find the height and breadth of the hall.
Summary:
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 25 m, the height and breadth of the hall are 8m and 10 m respectively
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