2017 · Q70
A cylinder of height 2x is circumscribed by a sphere of radius 2x such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere ?
Elementary MathematicsMensuration
- A√(3) : 4
- B√(3) : 3
- C√(3) : 2
- D√(3) : 1
Explanation
The sphere has radius 2x and the cylinder height 2x, so half-height is x. Cylinder radius r satisfies r²+x² = (2x)², i.e. r = x√3. Curved surface = 2πr(2x) = 4√3πx²; sphere surface = 4π(2x)² = 16πx². Ratio = √3:4. Hence option (A) √(3):4.