Class 10 - Chapter 11: Areas Related to Circles

Section A (1 Mark each)

Q1. The area of a segment of a circle is less than the area of its corresponding sector. This statement is true for:

(a) Major segment only (b) Minor segment only (c) Both major and minor segments (d) None of these

Q2. Area of the minor segment of a circle of radius $r$ and central angle $\theta$ is given by:

(a) $\frac{1}{2}r^2 \sin \theta$ (b) $\frac{\theta}{360}\pi r^2 - \frac{1}{2}r^2 \sin \theta$ (c) $\frac{\theta}{360}\pi r^2 + \frac{1}{2}r^2 \sin \theta$ (d) $\frac{\theta}{360}\pi r^2$

Q3. A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segment is (Use $\pi = 3.14$):

(a) $28.5$ cm$^2$ (b) $38.5$ cm$^2$ (c) $78.5$ cm$^2$ (d) $50$ cm$^2$

Q4. Assertion (A): The area of a segment of a circle is defined as the area of the corresponding sector minus the area of the corresponding triangle.
Reason (R): A segment is the region bounded by a chord and the corresponding arc.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is $90^\circ$.

Solve on white paper.

Q6. A chord of a circle of radius 10 cm subtends an angle of $60^\circ$ at the centre. Find the area of the corresponding minor segment. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

Solve on white paper.

Q7. Find the area of the major segment of a circle of radius 35 cm and chord subtending an angle of $90^\circ$ at the centre.

Solve on white paper.

Section C (3 Marks each)

Q8. A chord of a circle of radius 12 cm subtends an angle of $120^\circ$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

Solve on white paper.

Q9. Find the area of the shaded region in the figure, where ABCD is a square of side 14 cm and two semicircles are drawn internally with AD and BC as diameters.

Solve on white paper.

Section D (5 Marks)

Q10. A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per cm$^2$. (Use $\sqrt{3} = 1.7$)

Solve on white paper.

Section E (4 Marks)

Q11. Case Study:

In a rangoli competition, a student made a design using a circle and an equilateral triangle inscribed in it. The radius of the circle is 32 cm.

(i) Find the area of the circle.

(ii) Find the side of the equilateral triangle.

(iii) Find the area of the design (shaded region between circle and triangle).

Solve on white paper.