- The problem involves finding the area of a shaded region formed by two overlapping circles.
- Each circle has a radius of 10 cm, and their centers are 10 cm apart.
- The shaded region is the intersection of the two circles.
- To find the area of intersection, we calculate the area of two circular segments.
- The angle subtended by the chord at the center of each circle is 120 degrees (since the triangle formed by the two centers and an intersection point is equilateral).
- The area of one circular segment is: (θ/360) * π * r² - (1/2) * r² * sin(θ), where θ = 120° and r = 10 cm.
- Plugging in the values: (120/360) * π * 100 - (1/2) * 100 * sin(120°) = (100π/3) - 50 * (√3/2) = (100π/3) - 25√3.
- Since there are two identical segments, the total shaded area is 2 * [(100π/3) - 25√3] = (200π/3) - 50√3 cm².
Parent Tip: Review the logic above to help your child master the concept of acid nomenclature worksheet.
