CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set D

Question. If the perimeter of a semi-circular protractor is 36 cm, then its diameter is:
(a) 12 cm
(b) 13 cm
(c) 14 cm
(d) 15 cm
Answer : C

Question. The perimeter of a quadrant of a circle of radius ‘r' is: 
(a) πr/2
(b) 2πr
(c) r/2 [π + 4]
(d) 2πr + r/2
Answer : C

Question. The area of a circle, whose circumference is 22 cm, is: 
(a) 54 cm²
(b) 46 cm²
(c) 40.5 cm²
(d) 38.5 cm²
Answer : D

Question. If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then:
(a) R1 + R₂ = R
(b) R₁₂ + R₂₂ = R₂
(c) R1 + R₂ < R
(d) R₁₂ + R₂₂ < R₂
Answer : B

Question. If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then:
(a) R₁ + R₂ = R
(b) R₁ + R₂ > R
(c) R₁ + R₂ < R
(d) Nothing definite can be said about the relation among R₁ R₂ and R. 
Answer : A

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 would be:
(a) 10 m
(b) 15 m
(c) 20 m
(d) 24 m
Answer : A

Question. The radii of two concentric circles are 4 cm and 5 cm. The difference in the areas of these two circles is: 
(a) π
(b) 7 π
(c) 9 π
(d) 13 π
Answer : C

Question. If the area of a circle is 154 cm², then its circumference is: 
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm
Answer : C

Question. A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is: (π = 22/7)
(a) 22 cm
(b) 33 cm
(c) 44 cm
(d) 66 cm
Answer : B

Question. The area of a circle that can be inscribed in a square of side 6 cm is:
(a) 36 p cm²
(b) 18 p cm²
(c) 12 p cm²
(d) 9 p cm²
Answer : D

Question. The outer and inner diameters of a circular ring are 34 cm and 32 cm respectively. The area of the ring is: 
(a) 66p cm²
(b) 60p cm²
(c) 33p cm²
(d) 29p cm²
Answer : C

Question. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is:
(a) 31 cm
(b) 25 cm
(c) 62 cm
(d) 50 cm
Answer : D

Question. If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the area of the path is
(a) 1450 m²
(b) 1576 m²
(c) 1694 m²
(d) 3368 m²
Answer : C

Question. If a square ABCD is inscribed in a circle of radius ‘r' and AB = 4 cm, then the value of r is:
(a) 2 cm
(b) 2√2 cm
(c) 4 cm
(d) 4√2 cm
Answer : B

Question. The radius of a circle whose circumference is equal to the sum of the circum ferences of the two circles of diameters 36 cm and 20 cm is:
(a) 56 cm
(b) 42 cm
(c) 28 cm
(d) 16 cm
Answer : C

Fill in the Blanks

Fill in the blanks/tables with suitable information:

Question. The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal is ......................
Answer : π/√3

Question. The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km is ......................
Answer : 7000

Question. The area of the circle inscribed in a square of side a cm is ...................... .
Answer : (πa²/4) cm²

Question. If circumference and the area of a circle are numerically equal, then the diameter of the circle is ...................... .
Answer : 4 units

Question. If the circumference of a circle is 66 cm, then is its area is ...................... .
Answer : 86.625 cm²

Question. If the area of circle is 616 cm², then its circumference is ...................... .
Answer : 88 cm

Question. If the area of a semi-circlular region is 308 sq cm, then its perimeter is ......................... 
Answer : 72 cm]

Question. Number of rounds that a wheel of diameter 7/11 metre will make in moving a distance of 2 km is ............... 
Answer : [1000 rounds]

Case Study Based Questions

I. A student of class X standard finds in a circular table cover with radius 32 cm, a design which is formed leaving an equilateral triangle ABC in the middle as shown in the figure. Some questions arises in his mind which he shares with you. Help him to solve these questions.

Question. What is the area of the circular table?
(a) (22528/7) cm²
(b) (20528/7) cm²
(c) (22028/7) cm²
(d) (28022/7) cm²
Answer : A

Question. What is the measure of angle subtended by each side of the equilateral triangle at the centre of the circle?
(a) 30°
(b) 60°
(c) 120°
(d) 90°
Answer : C

Question. Each side of the equilateral triangle is
(a) 64√3 cm
(b) 8√3 cm
(c) 16√3 cm
(d) 32√3 cm
Answer : D

Question. What is the area of equilateral triangle?
(a) 700 3√2 cm
(b) 768 3√2 cm
(c) 678 3√2 cm
(d) 876 3√2 cm
Answer : B

Question. What is the area of the design?
(a) 1888 cm²
(b) 1688 cm²
(c) 1988 cm²
(d) 1588 cV
Answer : A
 

II. Some students of class-Xth get together and decide to form a design by combining different
mathematical shapes. First of all they select a triangle ABC with AB = 3 cm, AC = 4 cm and ∠BAC
= 90°. They draw semicircles on sides AB, AC and BC but they have some doubts which they want
to clarify with you. So, answer their questions given below:

Question. The length of side BC is
(a) 5 cm
(b) 25 cm
(c) 9 cm
(d) 16 cm
Answer : B

Question. Area of semicircle on side AB is
(a) (3/2)π cm²
(b) (9/8)π cm²
(c) 9π cm²
(d) 4π cm²
Answer : C

Question. Area of semicircle on side AC is
(a) 4π cm²
(b) 2π cm²
(c) 9π cm²
(d) 16π cm²
Answer : D

Question. Area of given figure is
(a) (9/4 π+6) cm²
(b) (16π/9 + 6) cm²
(c) (25π/8 + 6) cm²
(d) (4π/25 + 6) cm²
Answer : B

Question. Find the area of the shaded region.
(a) 6 cm²
(b) 8 cm²
(c) 10 cm²
(d) 12 cm²
Answer : A

1) A bicycle wheel makes 5000 revolution in moving 11 km. find the diameter of the wheel (d = 70 cm)

2) In the figure o is the centre of a circle. The area of sector OAPB is 5/18 of the area of the circle. Find x p

(100˚) x A B

3) Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor arc (60˚)

4) If the diameter of a semi circle protractor is 14 cm. Find its perimeter (36cm)

5) The circumference of a circle A is 132cm. It is equal to the sum of the circumference of two circles B & C, the radius of the circle

B is 14cm. Find the radius of circle C. (r = 7 cm)

6) The area of quadrant is 154sq cm. Find its perimeter. (50 cm)

7) A circular disc of 6cm radius is divided into 3 sectors with central angles 120˚, 150˚and 90˚.Find the ratio of the areas of 3 Sectors (4: 5: 3)

8) The difference between circumferences and diameter of a circle is 105 cm. Find the radius of the circle (24.5 cm)

9) Find the area of a major sector of a circle of diameter 42 cm and central angle is 60˚ (1155cm2)

10) If the area and circumference of a circle are numerically equal, then find the radius of the circle (2cm)

11) The length of a rope by which a cow is tethered is increased from 16m to 23m. How much additional area can the cow graze? Now (π =22/7) (2.38 Ѳm2)

12) What will be the increase in area of circle if its radius is increased by 40% (96%)

13) The radius of the wheel of a bus is 70cm, how many revolutions per minute must a wheel make in order to move at a speed of 66 km/h (250)

14) An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2 . Find the radius of the circle (8cm)

15) The circumference of a circle exceeds the diameter by 16.8cm. Find the radius of circle (3.92cm)

16) The area enclosed between two concentric circles is 770 sq cm. If the radius of outer circle is 21cm. Find the radius of the inner circle. (14 cm)

17 The length of the minute hand of a clock is 7cm. How much area does it sweep in 20minutes (154/3 cm2)

18) The perimeter of a sector of a circle of radius 5.2cm is 16.4cm.Find the area of sector (15.6cm2)

19) Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB. (84. 85 cm2)

20) Length of minor arc of a circle of radius 10 cm is 14cm. Find the area of minor sector of a circle. (70cm2)

21) A chord AB of a circle of radius 14cm makes a right angle at the centre of the circle. Find the area of the minor segment. (π = 22/7) (56 cm2)

22) Find the area of the major segment APB, in figure of a circle of radius 35 cm and ∟AOB = 90˚ (π = 22/7) P (3500 cm2) A B

23) A chord of a circle of radius 14cm subtends an angle of 120˚ at the centre Find the area of the corresponding minor segment of

The circle (π = 22/7, √3 = 1.73) (120.56 cm2 )

24) From a thin metallic piece, in the shape of a trapezium ABCD in which AB II CD and ∟BCD = 90˚, a quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2cm, calculate the area of the remaining (shaded) part of the metal sheet (π = 22/7)

Please click the below link to access CBSE Class 10 Mathematics Worksheet - Areas related to Circles (3)