Question
Two concentric circles drawn with the radius of inner circle 6cm and outer circle radius 50% more than inner circle. What is the area of the annulus formed between two circles?
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
$\frac{990}{7}\text{ cm}^2$
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.
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