2020 · Q88
A right circular cylinder just encloses a sphere. If p is the surface area of the sphere and q is the curved surface area of the cylinder, then which one of the following is correct?
Elementary MathematicsMensuration
- Ap = q
- Bp = 2q
- C2p = q
- D2p = 3q
Explanation
The enclosing cylinder has radius R and height 2R. Then p = 4πR² and q = 2πR × 2R = 4πR², so p = q. This is Archimedes' classical result that a sphere and its circumscribing cylinder have equal surface area.