2025 · Q60
Consider the following for the next two (02) items that follow: A pot is made from a hollow sphere of inner radius 20 cm by cutting its upper portion horizontally. The height of the pot is 30 cm. What is the angle made by the line joining the centre of the sphere and any point on the rim of the circular opening with a vertical line passing through the centre?
Elementary MathematicsMensuration
- Aπ/3
- Bπ/4
- Cπ/6
- Dπ/12
Explanation
The sphere's centre is 20 cm above the pot's base, while the rim at height 30 cm is 10 cm above the centre. The rim radius is sqrt(20^2 - 10^2) = sqrt(300) = 10*sqrt(3) cm. If theta is the angle between the centre-to-rim line and the vertical, tan(theta) = 10*sqrt(3)/10 = sqrt(3), so theta = pi/3. Hence option (a).