2022 · Q71
Consider the following for the next three (03) items that follow: A conical vessel has radius 12 cm and height 16 cm. A sphere is inscribed in the cone. What is the radius of the sphere?
Elementary MathematicsMensuration
- A5 cm
- B6 cm
- C6.5 cm
- D7 cm
Explanation
The axial cross-section is a triangle with base 24, height 16 and equal sides 20 (slant height √(12²+16²)); its inradius is area/semiperimeter = (192)/(32) = 6 cm, which is the inscribed sphere's radius. A frequent error is to use the cone's slant height in the inradius formula instead of the axial triangle's semiperimeter. The keyed option is B.