2016 · Q50
A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains 1408/21 m³ of air. What is the height of the building?
Elementary MathematicsMensuration
- A6 m
- B4 m
- C3 m
- D2 m
Explanation
Let the base radius be r: total height = h_cyl+r = 3r gives h_cyl = 2r. Volume = πr²(2r)+(2/3)πr³ = (8/3)πr³ = 1408/21, so r³ = 8 and r = 2. The building's height is 3r = 6 m (option A).