Question

A circular hall, surmounted by a hemispherical roof, contains 5236 m³ of air. If the internal diameter of the room is equal to the height of the highest point of the roof from the floor, find the height of the hall. 

Answer 1

diameter of the room = height of the hall ⇒ 2r = h 

Volume of the hall = 

But r = `h/2`

⇒ `pih^2/4h + 2/3pih^3/8 = 5236`

⇒ `pih^3/4 + 2/24pih^3 = 5236`

⇒ `pih^3(1/4 + 2/24) = 5236`

⇒ `pih^3 = (5236 xx 24)/8`

⇒ `h^3 = (5236 xx 24 xx 7)/(8 xx 22)`

⇒ `h^3 = 4998`

⇒ h = 17.09 m

Height of the hall = 17 .09 m