1) The shaded region is an annulus (ring) formed by two concentric circles.
- Outer radius R = 7 cm
- Inner radius r = 4 cm
Area of annulus = πR² - πr² = π(R² - r²) = π(49 - 16) = 33π cm²
2) The bigger circle has radius 16 cm. The smaller circle passes through the center O and touches the bigger circle, so its diameter equals the radius of the bigger circle.
- Radius of bigger circle R = 16 cm
- Radius of smaller circle r = 8 cm (since diameter = 16 cm)
Shaded area = Area of big circle - Area of small circle = πR² - πr² = π(256 - 64) = 192π cm²
3) The circle has diameter 40 cm, so radius r = 20 cm.
The isosceles triangle has its base as the diameter of the circle and vertex on the circumference. Since the base is the diameter, the triangle is right-angled at the vertex (Thales’ theorem).
- Base = 40 cm, height = 20 cm (radius perpendicular to diameter at center)
Area of triangle = (1/2) × base × height = (1/2) × 40 × 20 = 400 cm²
Area of circle = πr² = π × 400 = 400π cm²
Shaded area = Area of circle - Area of triangle = 400π - 400 = 400(π - 1) cm²
Parent Tip: Review the logic above to help your child master the concept of shaded area problems geometric probability worksheet.
