Class 10 - Chapter 11: Areas Related to Circles

Section A (1 Mark each)

Q1. Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is:

(a) $\frac{p}{180} \times 2\pi R$ (b) $\frac{p}{180} \times \pi R^2$ (c) $\frac{p}{360} \times 2\pi R$ (d) $\frac{p}{720} \times 2\pi R^2$

Q2. The angle described by the minute hand of a clock between 8 AM and 8:25 AM is:

(a) $150^\circ$ (b) $120^\circ$ (c) $100^\circ$ (d) $180^\circ$

Q3. If the area of a sector is $\frac{7}{20}$ of the area of the circle, then the sector angle is:

(a) $110^\circ$ (b) $126^\circ$ (c) $100^\circ$ (d) $120^\circ$

Q4. Assertion (A): In a circle of radius 6 cm, the angle of a sector is $60^\circ$. The area of the sector is $18.84$ cm$^2$ (Take $\pi = 3.14$).
Reason (R): Area of a sector of a circle with radius $r$ and angle $\theta$ is $\frac{\theta}{360} \times \pi r^2$.

(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 a sector of a circle with radius 6 cm if the angle of the sector is $60^\circ$.

Solve on white paper.

Q6. Find the area of a quadrant of a circle whose circumference is 22 cm.

Solve on white paper.

Q7. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Solve on white paper.

Section C (3 Marks each)

Q8. In a circle of radius 21 cm, an arc subtends an angle of $60^\circ$ at the centre. Find: (i) the length of the arc, (ii) area of the sector formed by the arc.

Solve on white paper.

Q9. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^\circ$. Find the total area cleaned at each sweep of the blades.

Solve on white paper.

Section D (5 Marks)

Q10. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find:
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use $\pi = 3.14$)

Solve on white paper.

Section E (4 Marks)

Q11. Case Study:

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors.

(i) Find the total length of the silver wire required.

(ii) Find the area of each sector of the brooch.

(iii) If the diameter of the brooch is doubled, keeping the number of sectors the same, what will be the new area of each sector?

Solve on white paper.