A hall is 15m long and 12m broad, the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls. Find the volume of the hall?

Sum of areas of 4 walls = Sum of areas of floor and ceiling.

Area of wall adjacent to the breadth of the room = Breadth ✕ Height = 12 ✕ h , there are 2 such walls

Area of wall adjacent to the length of the room = length of wall ✕ Height = 15 ✕ h, there are 2 such walls

Area of roof = 15 ✕ 12

Area of floor = 15 ✕ 12

12 ✕ h + 12 ✕ h + 15 ✕ h + 15 ✕ h = 15 ✕ 12 + 15 ✕ 12

2 ✕ 12 ✕ h + 2 ✕ 15 ✕ h = 2 ✕ 15 ✕ 12

2 (12 ✕ h + 15 ✕ h) = 2 (15 ✕ 12)

27h = 15 ✕ 12

Therefore, height h = 20/3 m

Therefore volume = Length ✕ Breadth ✕ Height

= 15 ✕ 12 ✕ (20/3)

= 1200 cubic metres.

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