SSC GD 2024 PYQ — Question 42

The correct answer is option 2 i.e. 24.64 cm²

 Circumference of a circle: $C = 2\pi r$

 Diameter of a circle: ( D = 2r)

 Area of a circle:  $A = \pi r^2$

The difference between the circumference and the diameter is 12 cm. 

⇒ C - D = 12

⇒ $2\pi r - 2r = 12$

⇒ $2r(\pi - 1) = 12$ 

⇒ $r = \frac{12}{2(\pi - 1)} = \frac{6}{\pi - 1}$

⇒ A = $\pi r^2$

⇒ A = $\pi \left(\frac{6}{\pi - 1}\right)^2$

⇒ A = $\pi \times \frac{36}{(\pi - 1)^2}$

⇒$A \approx 3.1416 \times \frac{36}{(3.1416 - 1)^2} \approx 3.1416 \times \frac{36}{2.1416^2}$

⇒ $\approx 3.1416 \times \frac{36}{4.585} \approx 3.1416 \times 7.85 \approx 24.64 \, \text{cm}^2$