A hall is 15m long and 12m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the 4 walls, what is the volume of the hall?
Answer: 1200 Cu.m
Explanation
Square = 4 sides are equal
Rectangle = only 2 opposite sides are equal
In the case of 3-dimension,
If the hall is in Cube shape, the area of all 4 walls will be equal.
But, here we know that the hall is in a Rectangular Prism shape, so only the area of 2 opposite walls will be equal.
Area of two walls = 15*b + 15*b = 30b
Area of other two walls = 12*b + 12*b = 24b
Hence,
Their Sum = 30b + 24b = 54b
360 = 54b which means b = 360/54 = 20/3
Here, the breadth of the walls is equal to the height of the rectangular prism (Hall)
Hence,
Volume of Hall = l*b*h = 15*12*(20/3) = 1200 cu.m
