2024 · Q93
Three identical cones each with base radius 3 cm are placed on their bases so that each is touching the other two. There will be one and only circle that would pass through each of the vertices of the cones. What is the area of the circle?
Elementary MathematicsCircles
- A3π square cm
- B6π square cm
- C9π square cm
- D12π square cm
Explanation
The three cones touch pairwise, so their base centres form an equilateral triangle of side 3+3 = 6 cm. The unique circle through the three vertices lies in the plane of the apexes, directly above the base centres, with radius equal to the triangle's circumradius 6/√3 = 2√3 cm. Its area is π(2√3)² = 12π sq cm — option D.