Assignments for Class 10 Mathematics Areas related to Circles have been developed for Standard 10 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 10 Mathematics Areas related to Circles from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 10 Mathematics Areas related to Circles. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Areas related to Circles book and get good marks in class 10 exams.

**Question. The ratio of the outer and inner perimeters of a circular path is 23: 22. If the path is 5 meters wide, the diameter of the of the inner circle is **

(A) 55 m

(B) 110 m

(C) 220 m

(D) 230 m

**Answer**

C

**Question. If the sum of the areas of two circles with radii r _{1} and r_{2} is equal to the area of a circle of radius r, then **

(A) r=r

_{1}+r

_{2}

(B) r

^{2}

_{1}+r

^{2}

_{2}=r

^{2}

(C) r

_{1}+r

_{2}<r

(D) r

_{1}

^{2}+r

_{2}

^{2}<r

^{2}

**Answer**

B

**Question. If the sum of the circumferences of two circles with radii r _{1}+r_{2} is equal to the circumference of a circle of radius r, then **

(A) r=r

_{1}+r

_{2}

(B) r

_{1}+r

_{2}>r

(C) r

_{1}+r

_{2}<r

(D) None of these

**Answer**

A

**Question. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is **

(A) 50√2cm

(B) (100 /π )cm

(C) (50√2/π )cm

(D) (100√2 π )cm

**Answer**

C

**Question. The area of the incircle of an equilateral triangle is 154 cm2. The perimeter of the triangle is **

(A) 71.5 cm

(B) 71.7 cm

(C) 72.3 cm

(D) 727 cm

**Answer**

D

**Question. If the circumference of a circle increase from 4π to 8π , then its area is **

(A) halved

(B) doubled

(C) tripled

(D) quadrupled

**Answer**

D

**Question. If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of π , is **

(A) π :√3

(B) 2:√π

(C) 3:π

(D) π :√2

**Answer**

D

**Question.ABCD is a square of side 4 cm . If E is a point in the interior of the square such that CED is equilateral , then area of ACE is **

(A) 2(√3–)cm2

(B) 2 4(√3 –1)cm

(C) 2 6(√3–1)cm

(D) 2 8(√3–1)cm

**Answer**

B

**Question. If π is taken as 22/7 , the distance (in meters) covered by a wheel of diameter 35 cm, in one revolution, is **

(A) 2.2

(B) 1.1

(C) 9.625

(D) 96.25

**Answer**

B

**Question. If AB is a chord of length 5 3cm of a circle with centre O and radius 5 cm, then area of sector OAB is **

(A) 3π/8 cm^{2}

(B) 3π/3 cm^{2}

(C)25π cm^{2}

(D)25π/3cm^{2}

**Answer**

D

**VERY SHORT ANSWER TYPE QUESTIONS**

**Question. In figure, what is the area of shaded region when ABCD is a square of side 14 cm. **

**Answer**

42 cm^{2}

**Question. In figure, ABCD is a square of side 7 cm. What is the area of the shaded region? **

**Answer**

10.5 cm^{2}

**Question. A wire is in the form of a circle of radius 14 cm. It is bent into a square. Determine the side of the square.**

**Answer**

22 cm

**Question. If an arc forms 120° at the centre O of the circle. What is the ratio of its length to the circumference of the circle?**

**Answer**

1 : 3

**Question. The archery target has three concentric circular regions. The diameter of the regions are in the ratio 1 : 2 : 3. What is the ratio of their areas?**

**Answer**

1 : 4 : 9

**Question. A bicycle wheel makes 10 revolutions in moving 880 cm. What is the radius of the wheel?**

**Answer**

14 cm

**Question. In figure, what is the area of the shaded region included between two concentric circles? **

**Answer**

269.5 cm^{2}

**Question. In figure, OACB is a quadrant of a circle of radius 14 cm. What is its perimeter? **

**Answer**

50 cm

**Question. What is the radius of a circle whose circumference and area are numerically equal?**

**Answer**

2 units

**Question. In figure, find the area of the shaded region. **

**Answer**

42 cm^{2}

**Question. If the perimeter of a protractor is 72 cm, what is its radius?**

**Answer**

14 cm

**Question. In figure, given a sector of a circle of radius 10.5 cm. What is the perimeter of the sector? **

**Answer**

32 cm

**Question. What is the area of a sector of a circle with diameter 21 cm and central angle 120°?**

**Answer**

115.5 cm^{2}

**Question. What is the area of the largest triangle that can be inscribed in a semicircle of radius a cm?**

**Answer**

a^{2} cm^{2}

**Question. The length of a minute hand of a wall clock is 7 cm. What is the area swept by it in half an hour?**

**Answer**

77 cm^{2}

**Areas Related To Circle**

**For a circle of radius = r units, we have :**

a) Circumferences of the circle (2πr ) units

b) Area of the circle (πr^{2}) sq. units.

c) Area of the semicircle 1/2(πr^{2} ) sq. units.

d) Perimeter of the semicircle (πr+2r) unirt

**Area of a Circular Ring :** If R and r be the outer and inner radii of a ring, than area of the

ring =π (R^{2}-r^{2})sq. units. =π (R+r)(R+r) sq. units.

**Length of Arc and Area of Sector :**

Area of sector (AOBC)= angle/360^{0}×π×(r)×(r)

Length of an arc (ABC)= angle/360^{0}×2π×(r)

Perimeter of a sector = angle/360^{0}×2π×(r)+2(r)

Area of segment = Area of corresponding sector – area of corresponding triangle F

**Rotating Wheels**

a) Distance moved by a wheel in 1 revolution = Circumference of the wheel.

Number of rotations made by wheel in unit time = Distance of moved in unit time / circumference of the wheel.

**PRACTICE EXCERCISE**

**Question. A horse is placed for grazing inside a rectangular field 80 m by 55 m and is tethered to one corner by a rope 21 m long. On how much area can it graze?****Solution.** 346.5 m^{2}

**Question. Find the area of the shaded region in the figure if AC=24cm,BC=10cm and ‘o’ is the center of the circle (use π = 3.14) **

**Solution.** 145.33 cm^{2}

**Question. The inner circumference of a circular track is 440m.The track is 14m wide. Find the diameter of the outer circle of the track. [Take π=22/7]****Solution.** D= 160 m

**Question. Find the area of the shaded region. **

**Solution.** 4.71 cm^{2}

**Question. Two circles touch externally the sum of the areas is 130π cm ^{2} and distance between there centre is14cm. Find the radius of circle.**

**Solution.**11 cm and 3 cm

**Question. Two circle touch internally. The sum of their areas is116π cm²distance between their centres is 6cm. Find the radii of circles.****Solution.** 4 cm and 10 cm

**Question. ABC is a quadrant of circle of radius14cm and a semi-circle is drawn with BC as diameter. Find the area of Shaded region.**

**Solution.** 98 cm^{2}

**Question. The length of a minor arc is 2/9 of the circumference of the circle. Write the measure of the angle subtended by the arc at the centre of the circle.****Solution.** 80°

**Question. A wire is looped in the form of a circle of radius 28cm.It is rebent in to a square form. Determine the side of the square(use π =22/7)****Solution.** 44 cm

**Question. An Umbrella has 8 ribs which are equally spaced. Assume Umbrella to be flat circle of radius 45cm find the area between two consecutive ribs of umbrella.(use π =3.14)****Solution.** 794.81 cm^{2}

**Question. A child prepare a poster on “save energy” on a square sheet whose each side measure 60cm. at each corner of the sheet, she draw a quadrant of radius17.5cm in which she shows the ways to save energy at the centre. She draws a circle of diameter 21cm and writes a slogan in it. Find the area of remaining sheet.(use π=3.14)****Solution.** Area of Remaining sheet=2292.19cm^{2}

**Question. A birthday cake is circular in shape. This cake is equally divided among six friends where radius of the cake is 60cm.(use π=3.14)****FInd the area of each piece of cake****Solution. **Area of each piece=1884cm^{2}

**Question. Three horses are tethered with 7m long ropes at the three corners of a triangular field having sides 20m, 34m 42m.Find the area of the plot.****i. Grazed by horses****ii. Remains un grazed by horses****Solution.** (i) 77 m^{2}

(ii) 259 m^{2}

**Question. A pendulum swings through an angle of 300 and describes an arc 8.8cm in length. Find length of pendulum.****Solution.** 16.8 cm

**Question. A copper wire when bent in the form of a square encloses an area of 121cm ^{2}.If the same wire is bent in to the form of a circle, find the area of the circle(use π =22/7)**

**Solution.**154 cm

^{2}

**Question. Calculate the area of shaded region in given figure where ABCD is square of side 16cm. **

**Solution.** 109.7 cm^{2}

**Question. The area of an equilateral triangle is 49√3cm ^{2}. Taking each angular point as centre, circle is drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take √3=1.73]**

**Solution.**7.77 cm

^{2}

**Question. In figure ‘o’ is the centre of a circle. The area of sector OAB is 5/18 of the area of the circle find x. **

**Solution.** 100°

**Question. If the diameter of a semicircular protractor is 14cm, then find its perimeter.****Solution.** 36 cm

**Question. The diameter of a cycle wheel is 21cm.How many revolutions will it make to travel 1.98km?****Solution.** 3000

**Question. The length of the minute hand of a clock is 14cm.Find the area swept by the minute hand in 5 minutes.****Solution.** 154/3 cm^{2}

**Question. The side of a square is10cm find the area of circumscribed and inscribed the circle.****Solution.** 50 π cm^{2}, 25 π cm^{2}

**Question. Find the area of the shaded region, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle. **

**Solution.** 161.54 cm^{2}

**Question. An athletic track 14 m wide consists of two straight sections 120 m long joining semi-circulars ends whose inner radius is 35 m. Calculate the area of the shaded region. **

**Solution.** 7056 m^{2}

**Question. Find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles. **

**Solution. **42 cm^{2}

**Question. Find the area of the shaded portion : **

**Solution.** (i) 1137.5 cm^{2} (ii) 231 cm^{2}

**Question. The length of a minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.****Solution.** 30.8 cm^{2}

**Question. The area of an equilateral triangle is 49 √3 cm ^{2}. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown. Find the area of the triangle not included in the circle. **

**Solution. **7.77 cm^{2}

**Question. A chord AB of a circle of radius 6 cm subtends an angle of 60° at the centre O. Find the area of the minor segment ACB. **

**Solution.** 3.27 cm^{2}

**Question. If the area of a semi-circular region is 1,232 cm ^{2}, find its perimeter.**

**Solution.**144 cm

**Question. A wheel has diameter 84 cm. Find how many complete revolutions must it take to cover 1584 meters.****Solution.** 600

**Question. 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.****(iii) area of the segment formed by the corresponding chord. ****Solution.** Let O be the centre of the circle of radius 21 cm such that an arc APB subtends θ = 60° at the centre.

**Question. 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 as shown in the given figure. Find : ****(i) the total length of the silver wire required.****(ii) the area of each sector of the brooch.**

**Solution.**

**Question. The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the shaded region. [Use π = 3.14 and √3 =1.73205].**

**Solution.** We know, area of an equilateral triangle = √3/4 x (side)^{2}

**Question. Calculate the area of the designed region in the given figure common between two quadrants of circles of radius 8 cm each.**

**Solution.** Area of the designed region

= 2 (Area of quadrant ABED – Area of ΔABD)

**Question. In a circular table of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the figure. Find the area of the design (shaded region).**

**Solution.** In ΔOBD, we have OD/OB = cos 60° and BD/OB = sin 60°

**Question. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at the speed of 66 km per hour? ****Solution.** We have, Speed of the car = 66 km/hr

∴ Distance travelled by the car in 60 minutes = 66 km

⇒ Distance travelled by the car in 10 minutes = 66/20 x 10km

= 11 km = 1100000 cm

Also, diameter of car wheels = 80 cm

⇒ radius of car wheels 80/2 cm=40cm (= r say)

**Question. The given figure depicts a racing track whose left and right ends arc semicircular. The distance between the inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find : ****(i) the distance around the track along its inner edge.****(ii) the area of the track.**

**Solution.** (i) Distance around the track along its inner edge

= 2 × 106 m + Perimeter of two semi-circle of radius 60/2 m

**Question. In the given figure, an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameters of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.****Solution.** here,

r = radius of the region representing Gold score = 10.5 cm.

r_{1} = radius of the region representing Gold and Red scoring areas = 10.5 cm + 10.5 cm = 21 cm = 2r cm

r_{2} = radius of the region representing Gold, Red and Blue scoring areas = 21 cm + 10.5 cm = 31.5 cm = 3 r cm.

r_{3} = radius of the region representing Gold, Red, Blue and Black scoring areas = 31.5 cm + 10.5 cm = 42 cm = 4r cm.

r_{4} = radius of the region representing Gold, Red, Blue, Black and white scoring areas = 42 cm + 10.5 cm = 52.5 cm = 5r cm.

Now,

**Question. A round table cover has six equal designs as shown in the given 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 cm2 (use √3 = 1.7).**

**Solution.** Here, r = 28 cm and θ = 60° [∴ It is a regular hexagon]

∴ Required area = 6 × area of the segment ACB

= 6 × {area of the sector OACB – area of the equilateral ΔOAB}

**Question. 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 (see figure). Find ****(i) the area of that part of the field in which the horse can graze.****(ii) the increase in grazing area if the rope were 10 m long instead of 5m. (Use π = 3.14).**

**Solution.** Here r = 5 m, θ = 90°

(i) The area of the part AEFA of the field in

## Assignments for Class 10 Mathematics Areas related to Circles as per CBSE NCERT pattern

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