Answer:
The area of shaded is 72π cm² ⇒ answer A
Step-by-step explanation:
* Lets explain how to solve the problem
- The area of any circle is A = πr², where r is the radius of the circle
- The length of the radius of a circle is 1/2 the length of its diameter
- From the figure:
∵ There are two inscribed circles touch the larger circle internally
and touch each other externally
∴ The centers of the three circles are collinear
∴ The diameter of the larger circle = the sum of the diameters of
the two inscribed circles
∵ The radii of the inscribed circles are 4 cm and 9 cm
∵ The diameter = twice the radius
∴ The diameters of the inscribed circles are 2 × 4 = 8 cm and
2 × 9 = 18 cm
∴ The diameter of the larger circle = 8 + 18 = 26 cm
∵ The radius of the circle = 1/2 diameter
∴ The radius of the larger circle = 1/2 × 26 = 13 cm
- The area of the shaded part is the difference between the
area of the larger circle and the sum of the areas of the two
inscribed circles
∵ A = πr²
∴ The area of the larger circle = π(13)² = 169π
∵ The sum of areas of the inscribed circles = π(4)² + π(9)²
∴ The sum of areas of 2 circles =16π + 81π = 97π
∵ Area of shaded = A larger circle - sum of A of 2 circles
∴ Area of shaded = 169π - 97π = 72π
* The area of shaded is 72π cm²
