Two concentric circles drawn with the radius of inner circle 6 cm and outer circle radius 50% more than inner circle. What is the area of the annulus formed between two circles?

Correct option is D

Given:
Radius of the inner circle,  r = 6 cm.
Radius of the outer circle is 50% more than the inner circle.
Concept Used:
The area of a circle =$$\pi \times \text{radius}^2$$. The area of the annulus is the difference between the areas of the outer and inner circles.
Solution:
Since the outer circle's radius is 50% more than the inner circle's radius:
R = r + 0.5r = 1.5r $$= 1.5 \times 6 = 9 \text{ cm}$$

​$$\text{Area}_{\text{inner}} = \pi r^2 = \pi \times 6^2 = 36\pi \text{ cm}^2$$​​
$$\text{Area}_{\text{outer}} = \pi R^2 = \pi \times 9^2 = 81\pi \text{ cm}^2$$​
​$$\text{Area}_{\text{annulus}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 81\pi - 36\pi = 45\pi \text{ cm}^2$$ =$$\frac{45\times22}{7}=\frac{990}{7}$$cm²​​