Practice Questions: Areas Related to Circles | Mathematics (Maths) Class 10 PDF Download

Questions

1. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle (in cm).

2. The circumference of a circle is 22 cm. Calculate the area of its quadrant (in cm²). 

3. If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, calculate the circumference (in cm) of the circle. 

4. Find the area of a quadrant of a circle, where the circumference of circle is 44 cm. (Use π = 22/7] 

5. Area of a sector of a circle of radius 14 cm is 154 cm2. Find the length of the corresponding arc of the sector. [Use π = 22/7]

6. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) the length of the arc

(ii) area of the sector formed by the arc. [Use π = 22/7] 

7. Find the perimeter of the D shaded region in Figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles. [Use π = 22/7] 

8. In Figure, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. [Use π = 22/7]

9. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semi-circular portion with BC as diameter is cut off. Find the area of the remaining paper. (Use π = 22/7)

10. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm2. [Use π = 3.14]

11. The perimeter of a circle having radius 5cm is equal to _______________________.

12. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units

13. What is the area of a quadrant of a circle with circumference of 22 cm?

14. In a circle of radius 14 cm, an arc subtends an angle of 30° at the centre. What is the length of the arc?

15. If the area of a circle is 154 cm2, then its perimeter is
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm

Answers

1. Diameter = 26cm

2. 77/8 cm² 

3. Circumference of the circle = 44cm

4. Area of Quadrant = 38.5cm²  

5. 22cm

6. (i) 22cm

(ii) 231 cm²  

7. 72 cm

8. 10.5cm²    

9. Area of remaining paper = 812 sq.cm

10. Area of Rhombus = 800cm²   

11. 31.4 cm

12. (a) 2 units

13. Area of quadrant of a circle = 77/8 cm²  

14. 22/3 cm

15. (c) 44 cm