Answer :
The height of the auditorium is 30 meters. The correct answer is option B.
Given:
- The length and breadth of the auditorium are in the ratio 3:2.
- The area of the ceiling is 600 sq. m.
- The area of the four walls is 1500 sq. m.
Step 1: Calculate the length and breadth of the auditorium.
Let the length be 3x and the breadth be 2x, where x is a constant.
Area of the ceiling = 3x × 2x = 6x²
600 = 6x²
x = 5 meters
Length = 3x = 3 × 5 = 15 meters
Breadth = 2x = 2 × 5 = 10 meters
Step 2: Calculate the height of the auditorium.
Area of the four walls = 2(15 × 30) + 2(10 × 30) = 1500 sq. m
Height = 1500 / (2 × (15 + 10)) = 30 meters
Therefore, the height of the auditorium is 30 meters.
The correct answer is option B.
