Calculate Annulus Area

The problem asks for the area of the annulus formed between two concentric circles.

1. Determine the Radii

• Inner circle radius, $r_1$ = 6 cm.
• Outer circle radius, $r_2$, is 50% more than $r_1$.
• Calculation for $r_2$: $r_2 = r_1 + (0.50 \times r_1) = 6 \text{ cm} + (0.50 \times 6 \text{ cm}) = 6 \text{ cm} + 3 \text{ cm} = 9 \text{ cm}$.

2. Calculate Annulus Area

The area of an annulus is the difference between the area of the outer circle and the area of the inner circle.

Formula: Area $A = \pi (r_2^2 - r_1^2)$

• Substitute the radii values: $A = \pi (9^2 - 6^2)$ cm$^2$.
• Calculate the squares: $A = \pi (81 - 36)$ cm$^2$.
• Subtract: $A = \pi (45)$ cm$^2$.
• Use the approximation $\pi \approx \frac{22}{7}$: $A = \frac{22}{7} \times 45$ cm$^2$.
• Final calculation: $A = \frac{22 \times 45}{7} = \frac{990}{7}$ cm$^2$.

3. Final Answer

The area of the annulus formed between the two concentric circles is $\frac{990}{7}$ cm$^2$. This corresponds to Option D.