1) The shaded region is a ring (annulus) formed by two concentric circles. The area of a circle is given by the formula A = πr².
- Area of the larger circle: π × 7² = 49π cm²
- Area of the smaller circle: π × 4² = 16π cm²
- Area of the shaded region: 49π - 16π = 33π cm²
2) The shaded region is the area of the larger circle minus the area of the smaller circle.
- Radius of the larger circle: 16 cm
- Since the smaller circle passes through the center O of the larger circle and touches its circumference, its diameter equals the radius of the larger circle.
- Therefore, the radius of the smaller circle is 16 / 2 = 8 cm.
- Area of the larger circle: π × 16² = 256π cm²
- Area of the smaller circle: π × 8² = 64π cm²
- Area of the shaded region: 256π - 64π = 192π cm²
3) The shaded region is the area of the circle minus the area of the isosceles triangle.
- Diameter of the circle: 40 cm, so the radius is 20 cm.
- Area of the circle: π × 20² = 400π cm²
- The base of the isosceles triangle is the diameter of the circle (40 cm), and its height is equal to the radius (20 cm), since the apex lies on the circle and the base passes through the center.
- Area of the triangle: (1/2) × base × height = (1/2) × 40 × 20 = 400 cm²
- Area of the shaded region: 400π - 400 cm²
Parent Tip: Review the logic above to help your child master the concept of area of circle worksheet.
