#### Online Mock Tests

#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Liner Equation in Two Variable

Chapter 4: Quadatric Euation

Chapter 5: Arithematic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trignometry & its Equation

Chapter 9: Circles

Chapter 10: Construction

Chapter 11: Area Related To Circles

Chapter 12: Surface Areas and Volumes

Chapter 13: Statistics and Probability

## Chapter 11: Area Related To Circles

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 11 Area Related To Circles Exercise 11.1 [Pages 120 - 121]

#### Choose the correct alternative:

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 ______.

R

_{1}+ R_{2}= R`"R"_1^2 + "R"_2^2 < "R"^2`

R

_{1}+ R_{2}< R`"R"_1^2 + "R"_2^2 < "R"^2`

If the sum of the circumferences of two circles with radii R_{1} and R_{2} is equal to the circumference of a circle of radius R, then ______.

R

_{1}+ R_{2}= RR

_{1}+ R_{2}> RR1 + R2 < R

Nothing definite can be said about the relation among R

_{1}, R_{2}and R.

If the circumference of a circle and the perimeter of a square are equal, then ______.

Area of the circle = Area of the square

Area of the circle < Area of the square

Area of the circle > Area of the square

Nothing definite can be said about the relation between the areas of the circle and square.

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is ______.

r

^{2 }sq.units`1/2` r

^{2 }sq.units2 r

^{2 }sq.units`sqrt(2)` r

^{2 }sq.units

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

13 : 22

14 : 11

22 : 13

11 : 14

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 ______.

10 m

15 m

20 m

24 m

The area of the circle that can be inscribed in a square of side 6 cm, is ______.

36π cm

^{2}18π cm

^{2}12π cm

^{2}9π cm

^{2}

The area of the square that can be inscribed in a circle of radius 8 cm is ______.

256 cm

^{2}128 cm

^{2}`64sqrt(2)` cm

^{2}64 cm

^{2}

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is ______.

56 cm

42 cm

28 cm

16 cm

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 ______.

31 cm

25 cm

62 cm

50 cm

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 11 Area Related To Circles Exercise 11.2 [Pages 122 - 123]

#### State whether the following statement is True or False:

Is the area of the circle inscribed in a square of side a cm, πa^{2} cm^{2}? Give reasons for your answer.

True

False

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reasons for your answer.

True

False

In figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

True

False

Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why?

True

False

Is it true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2 π d cm? Why?

True

False

In covering a distance s metres, a circular wheel of radius r metres makes `s/(2 pir)` revolutions. Is this statement true? Why?

True

False

The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

True

False

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

True

False

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

True

False

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

True

False

Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is πb^{2} cm^{2}? Why?

True

False

Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

True

False

Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

True

False

Is it true to say that area of a square inscribed in a circle of diameter p cm is p^{2} cm^{2}? Why?

True

False

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 11 Area Related To Circles Exercise 11.3 [Pages 125 - 128]

#### Unless stated otherwise, use π = 22/7

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Find the area of a sector of a circle of radius 28 cm and central angle 45°.

The wheel of a motor cycle is of radius 35 cm . How many revolutions per minute must the wheel make so as to keep a speed of 66 km / hr ?

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions `20 m xx 16 m` find the area of the field in which the cow can graze .

Find the area of the flower bed (with semi-circular ends) shown in figure.

In figure, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use π = 3.14).

Find the area of the shaded field shown in figure.

Find the area of the shaded region in figure.

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD (Use π = 3.14).

In figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm. to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region (Use π = 3.14).

In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.

In figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.

A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle.

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 11 Area Related To Circles Exercise 11.4 [Pages 132 - 135]

The area of a circular playground is 22176 m^{2}. Find the cost of fencing this ground at the rate of Rs 50 per metre.

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.

Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60° (Use π = 3.14).

A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m^{2}

In figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

On a square cardboard sheet of area 784 cm^{2}, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)

All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm^{2}. (Use π = 3.14)

An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratios 1 : 2 : 3 , then find the ratio of the areas of three regions.

The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6:40 am.

Area of a sector of central angle 200° of a circle is 770 cm^{2}. Find the length of the corresponding arc of this sector.

The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

Find the area of the shaded region given in figure

Find the number of revolutions made by a circular wheel of area 1.54 m^{2} in rolling a distance of 176 m.

Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90° at the centre.

Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

## Chapter 11: Area Related To Circles

## NCERT solutions for Mathematics Exemplar Class 10 chapter 11 - Area Related To Circles

NCERT solutions for Mathematics Exemplar Class 10 chapter 11 (Area Related To Circles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 10 chapter 11 Area Related To Circles are Areas of Sector and Segment of a Circle, Area of Circle, Areas of Combinations of Plane Figures, Circumference of a Circle, Circumference of a Circle.

Using NCERT Class 10 solutions Area Related To Circles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

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