Mathematics exemplar problems class 10 Solutions for Chapter 11 areas related to circles

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

Area of the circle that can be inscribed in a square of side 6 cm 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

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

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

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

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

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

In covering a distance s metres, a circular wheel of radius r metres makes s/2πr revolutions. Is this statement true?

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm?

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

Is the area of the circle inscribed in a square of side a cm, a² cm²? Give reasons for your answer.

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

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 other circle. Is this statement false?

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

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 πb² cm²?

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

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

In the given 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?

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

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

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

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 the given 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?

In the given 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).

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

Find the area of shaded region in the given figure.

Find the area of the minor segment of circle of radius 14 cm, when the angle of 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 side AB, BC, CD and DA respectively of a square ABCD. (Use π = 3.14)

In the given 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 respectively. Find the are of the shaded region. (Use π = 3.14)

In the given figure, arcs have been drawn with radii 14 cm each and with centre 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 the given figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centre. Find the area of shaded region.

In the given figure, ABC is an equilateral triangle of side 8 cm. A, B and C are the centre of circular arcs of radius 4 cm. Find the area of the shaded region. (Take 𝛑 = 3.14 and √3 = 1.732)

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

Find the area of the shaded field shown in the given figure.

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

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 m²

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.

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.

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.

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.

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)

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

Find the area of the shaded region given in figure here.

Find the number of revolutions made by circular wheel of area 1.54 m² in rolling a distance of 176 m.

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

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

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

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.

In the given 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.

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

Find the area of the major segment of a circle formed by a chord of length 5 cm subtending angle of 90° at the centre.