2022 · Q18
What is the area of the region enclosed by three identical circles (each of radius 4 cm) touching each other?
Elementary MathematicsCircles
- A8π/3 square cm
- B((16√3 - 8π)/3) square cm
- C(16√3 - 8π) square cm
- D(16π)/3 square cm
Explanation
Joining the centres forms an equilateral triangle of side 8 cm with area (√3/4)x64 = 16√3 cm². From it subtract the three 60° sectors inside it: 3x(1/6)πx16 = 8π. The enclosed curvilinear region is 16√3-8π cm². The distractor (√3-8π)/3 wrongly divides by an extra 3. Hence the keyed option is C.