Solution of Chapter 11. Area Related To Circles (NCERT - Mathematics Exemplar Book)

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

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

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

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

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

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

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

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

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

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

Is the area of the circle inscribed in a square of side a cm, πa²cm²? Give reasons for your answer.

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

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 reason for your answer.

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

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

In covering a distance s m, a circular wheel of radius r m makes revolution. Is this statement true? Why?

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

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?

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

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

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 πb²cm? Why?

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

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

Is it true to say that area of a square inscribed in a circle of diameter p cm is p² cm²? Why?

Find the radius of a circle whose circumference is equal to the sum of the circumference 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/h?

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m × 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 centers A, B, C and D intersect in pairs at mid-point 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 centers 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, then 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 centers. Find the area of the shaded region.

The area of a circular playground is 22176 m². Find the cost of fencing this ground at the rate of `50 per m.

The diameter of front and rear wheels of a tractor are 80 cm and 2m, 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 17m. with the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7m 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 2m wide path. Find the cost of constructing the path at the rate of ` 25 per m²?

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 centers 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 cm², 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 5m × 4m and it is covered with circular tiles of diameters 50 cm each as shown in figure. Find 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 area of the circle is 1256 cm². (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 ratio 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 cm². Find the length of the corresponding arc of this sector.

The central angles of two sectors 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 m² 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 center.

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