NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.3

Question 2

Step 1: Understand the figure

The square is drawn inside the circle. The diagonal of the square is equal to the diameter of the circle.

Step 2: Find the side of the square

We know diagonal of square \(d = 8\,\text{cm}\).

Relation: \(d = s\sqrt{2}\), where \(s\) = side of square.

So, \(s = \dfrac{d}{\sqrt{2}} = \dfrac{8}{\sqrt{2}} = 4\sqrt{2}\,\text{cm}\).

Step 3: Area of the square

Formula: \(\text{Area} = s^2\).

Here, \(s = 4\sqrt{2}\).

So, \(s^2 = (4\sqrt{2})^2 = 16 \times 2 = 32\,\text{cm}^2\).

Step 4: Radius of the circle

Diameter of circle = diagonal of square = 8 cm.

So, radius \(r = \dfrac{8}{2} = 4\,\text{cm}\).

Step 5: Area of the circle

Formula: \(\pi r^2\).

Here, \(r = 4\,\text{cm}\).

So, area = \(\pi (4)^2 = 16\pi\,\text{cm}^2\).

Step 6: Area of shaded region

Shaded part = Area of circle − Area of square.

= \(16\pi - 32\,\text{cm}^2\).

Step 7: Approximate value (using \(\pi = 3.14\))

= \(16 \times 3.14 - 32\).

= \(50.24 - 32 = 18.24 \,\text{cm}^2\) (≈18.27 cm² after rounding).

Final Answer: \(16\pi - 32\,\text{cm}^2\) or approximately 18.27 cm².