Answer:
The height of the hall is 9.375 meters
Step-by-step explanation:
The rate at which the walls of the square hall are painted, R = Rs. 40 per sq. m.
The total cost of painting the square hall, C = Rs. 12,000
The volume of air contained in the hall, V = 600 m³
The surface area of the four walls of the hall, A = C/A
∴ A = Rs. 12,000/(Rs. 40/m²) = 300 m²
Let 's' represent the length of sides of the square hall, and let 'h' represent the height of the square wall, we have;
The volume of the hall, V = s² × h
The surface area of the wall, A = 4 × s × h
Therefore, we get;
A = 300 = 4 × s × h
V = 600 = s² × h
V/A = 600/300 = 2 = s² × h/(4 × s × h) = s/4
s/4 = 2
s = 4 × 2 = 8
The side length of the square hall, s = 8 m.
From the area, A = 4 × s × h, we get;
A = 300 = 4 × 8 × h
h = 300/(4 × 8) = 9.375
The height of the hall, h = 9.375 m.
