CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set F

Question. The perimeter (in cm) of a square circumscribing a circle of radius a cm is
(a) 2a
(b) 4a
(c) 6a
(d) 8a

Answer: D

Question. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park is
(a) 10 m
(b) 12 m
(c) 15 m
(d) 18 m

Answer: A

Question. The area of the largest triangle that can be inscribed in a semi-circle of radius r units will be
(a) r sq. units
(b) r /2 sq. units
(c) r² sq. units
(d) 2r sq. units

Answer: C

Question. In the given figure, O is the centre of the circle whose diameter is 14 cm.
Find the perimeter of the figure. (Use π = 22/7).
(a) 134cm
(b) 124cm
(c) 112cm
(d) 160cm

Answer: A

Question. A horse is tied to a pole with 28 m long rope. The perimeter of the field where the horse can graze is (Take π = 22/7)
(a) 60 cm
(b) 85 cm
(c) 124 cm
(d) 176 cm

Answer: D

Question. The area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm is
(a) 3.25 cm²
(b) 8.75 cm²
(c) 4.60 cm²
(d) 5.50 cm²

Answer: B

Question. The area of an equilateral triangle is 17320.5 cm2. With each vertex as centre, a circle is described with radius equal to half the length of the side of the triangle. The area of the triangle not included in the circles is (Use π = 3.14 and 3 = 1.73205).   
(a) 1620.51 cm²
(b) 1810.25 cm²
(c) 2430.60 cm²
(d) None of the options

Answer: A

Question. ABCD is a square of side 4 cm. At each corner of the square, a quarter circle of radius 1 cm, and at the centre, a circle of radius 1 cm, are drawn, as shown in the given figure. The area of the shaded region is   
(a) 8.46 cm²
(b) 7.25 cm²
(c) 9.71 cm²
(d) 10.43 cm²

Answer: C

Question. The radii of two circles are 8 cm and 6 cm respectively. The radius of the circle having area equal to the sum of the areas of the two circles is
(a) 5 cm
(b) 10 cm
(c) 12 cm
(d) 15 cm

Answer: B

Question. A regular hexagon is inscribed in a circle of radius 14 cm. Find the area of the circle falling outside the hexagon.   
(a) 106.79 cm²
(b) 241.8 cm²
(c) 79.27 cm²
(d) 173.9 cm²

Answer: A

Question. A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle 120°. The total area cleaned at each sweep of the blades is [Take π = 7/ 22 ]
(a) 360 cm²
(b) 448 cm²
(c) 556 cm²
(d) 924 cm

Answer: D

Question. If the perimeter and area of a circle are numerically equal; its radius will be
(a) 1 unit
(b) 2 units
(c) 4 units
(d) None of the options

Answer: B

Question. In a circular table cover of radius 32 cm, a design is formed having an equilateral triangle ABC in the middle, as shown below. The area of the design is   
(a) 777.36 cm²
(b) 1888.11 cm²
(c) 2010.54 cm²
(d) None of the options

Answer: B

Question. An athlete runs on a circular track of radius 49 m and covers a distance of 3080 m along its boundary. How many rounds has he taken to cover this distance ? [Take π = 22 / 7]
(a) 5
(b) 8
(c) 10
(d) 15

Answer: C

Question. A square shaped bus shelter is supported on four circular poles-The circumference of each pole is ‘x’ m and the length of each side of the shelter is ‘y’ m. Find the area of the unsupported part of the shelter.   
(a) (x² – y²/p)m²
(b) (y² + x²/p)m²
(c) (x² – y²/p)m²
(d) (y² – x²/p)m²

Answer: D

Question. The area of the largest circle that can be drawn inside the given rectangle of length ‘a’ cm and breadth ‘b’ cm (a > b) is
(a) 1/ 2 πb² cm²
(b) 1/ 3 πb² cm²
(c) 1/ 4 πb² cm²
(d) π b² cm²

Answer: C

Question. A wheel has diameter 84 cm. Number of complete revolutions must it make to cover 792 metres will be
(a) 100
(b) 160
(c) 220
(d) 300

Answer: D

Question. What is the area of the circle that can be inscribed in a square of side 6 cm?
(a) 9 π cm²
(b) 11 π cm²
(c) 16 π cm²
(d) 15 π cm²

Answer: A

Question. A sector of120° cut out from a circle has an area of 9 , 3/7 . What is the radius of the circle?
(a) 3cm
(b) 2.5 cm
(c) 3.5 cm
(d) 3.6 cm

Answer: A

Question. The difference of the areas of two segments of a circle formed by a chord of radius 5 cm subtending an angle of 90° at the centre is
(a) (25π/4 − 25/2) cm²
(b) (15π/ 4 − 7/ 2) cm²
(c) (7π/ 4 − 3/ 2) cm²
(d) None of the options

Answer: A

Question. The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences?
(a) 1 : 2
(b) 2 : 1
(c) 3 : 2
(d) 2 : 3

Answer: C

Question. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm²
(b) 128 cm²
(c) 64 √2 cm²
(d) 64 cm²

Answer: B

Question. A square ABCD is inscribed in a circle of radius 10 units. The area of the circle, not included in the square is (Take π = 3.14)   
(a) 84 cm²
(b) 108 cm²
(c) 114 cm²
(d) 122 cm

Answer: C

Question. Find the area of the sector of a circle, whose radius is 6 m when the angle at the centre is 42° .   
(a) 13. 2m²
(b) 14. 2m²
(c) 13. 4m²
(d) 14. 4m²

Answer: A

Question. The area of the shaded portion in the figure, given below, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre is   
(a) 156.64 cm²
(b) 188.46 cm²
(c) 256.64 cm²
(d) 310.25 cm²

Answer: A

Question. An arc of length 15.7 cm subtends a right angle at the centre of the circle. Then the radius of the circle is
(a) 20 cm
(b) 10 cm
(c) 15 cm
(d) 12 cm

Answer: B

Question. What is The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long?   
(a) 168 cm²
(b) 148 cm²
(c) 154 cm²
(d) 176 cm²

Answer: B

Question. The diameter of a circle whose circumference is equal to the sum of the circumference of the two circles of diameters 36 cm and 20 cm is
(a) 22 cm
(b) 32 cm
(c) 56 cm
(d) 84 cm

Answer: C

AREAS RELATED TO CIRCLES

MCQ

1. If the perimeter and area of a circle are numerically equal, then radius is

(a) 2 units (b) π units (c) 4 units (d) 7 units

2. Area of sector of circle with radius R and angle P is

(a) RPoπ2180× (b) 22180RPoπ× (c) RPoπ2360× (d) 22360RPoπ×

3. Length of the segement of a circle of radius R and angle P at centre is

(a) 22360RPoπ× (b) RPoπ2360× (c) 2360RPoπ× (d) RPoπ2180×

4. The difference between the circumference and the radius of the circle is 74 cm. The area of circle is

(a) 600 cm2 (b) 610 cm2 (c) 616 cm2 (d) 620 cm2

5. The circumference of a circle exceeds its diameter by 67.2 cm. The circumference of circle is

(a) 98.56 cm (b) 98 cm (c) 90 cm (d) 92 cm

6. The area of the two circles are in ratio 4 : 9. Ratio between their circumference is

(a) 1 : 2 (b) 2 : 3 (c) 3 : 4 (d) 4 : 5

7. The ratio of circumference of 2 circles is 3 : 1. Circumference of bigger circle is 39.36 cm, Radius of smaller circle is

(a) π2 cm (b) π5 cm (c) π56.6 cm (d) π23.1 cm

8. Find the distance covered by wheel of radius 21 dm when it makes 100 revolutions

(a) 1.32 km (b) 1.30 km (c) 1.31 km (d) 1.35 km

9. A car is moving with a speed of 22 decimetre/sec. Find the diameter of wheel if it performs 700 revolutions per second.

(a) 0.0 m (b) 0.2 m (c) 1.5 m (d) 0.1 m

10. If the perimeter of semicircular protractor is 36 cm. Its diameter is

(a) 10 cm (b) 12 cm (c) −15 cm (d) −14 cm

11. The perimeter of a circular field and a square field are same. Find the area of square field if area of circular field is 3850 m2.

(a) 3000 m2 (b) 4000 m2 (c) 3025 m2 (d) 3050 m2

12. The minute hand of a wall clock is of length 10.5 cm. Find area covered in 1 hour.

(a) 346.5 cm2 (b) 348.5 cm2 (c) 300.5 cm2 (d) 350 cm2

13. The inner circumference of a circular track is 24π. The track is 2 m wide everywhere. Find the quantity of wire required to surround the path completely

(a) 80 m (b) 81 m (c) 82 m (d) 88 m

14. The area of two concentric circles are 962.5 cm2 and 1386 cm2. The width of ring is

(a) 3.4 cm (b) 3.5 cm (c) 3.2 cm (d) 3.1 cm

Please click the below link to access CBSE Class 10 Mathematics Worksheet - Areas related to Circles (5)