Areas Related to Circles Class 10 Worksheets have been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 10. Students are always suggested to solve printable worksheets for Mathematics Areas related to Circles Grade 10 as they can be really helpful to clear their concepts and improve problem solving skills. We at worksheetsbag.com have provided here free PDF worksheets for students in standard 10 so that you can easily take print of these test sheets and use them daily for practice. All worksheets are easy to download and have been designed by teachers of Class 10 for benefit of students and is available for free download.

## Mathematics Areas Related To Circles Worksheets for Class 10

We have provided **chapter-wise worksheets for class 10 Mathematics Areas Related To Circles** which the students can download in Pdf format for free. This is the best collection of Mathematics Areas Related To Circles standard 10th worksheets with important questions and answers for each grade 10th Mathematics Areas Related To Circles chapter so that the students are able to properly practice and gain more marks in Class 10 Mathematics Areas Related To Circles class tests and exams.

### Chapter-wise Class 10 Mathematics Areas Related To Circles Worksheets Pdf Download

**Question. The area of a circle whose area and circumference are numerically equal, is **

(A) 2π sq.units

(B) 4π sq.units

(C) 6π sq.units

(D) 8π sq.units

**Answer**

B

**Question. If the area of a sector of a circle is 5/18 of the area of the circle, then the sector angle is equal to **

(A) 600

(B) 900

(C) 1000

(D) 1200

**Answer**

C

**Question. If the area of a sector of a circle is 7/20 of the area of the circle, then the sector angle is equal to **

(A) 1100

(B) 1300

(C) 1000

(D) 1260

**Answer**

D

**Question. The radius of circle is 20 cm. it is divided into four parts of equal area by drawing three concentric circles inside it. Then the radius of the largest of three concentric circles drawn is **

(A) 10√5cm

(B) 10√3cm

(C) 10 cm

(D) 10√2cm

**Answer**

B

**Question. The area of a sector whose perimeter is four times its radius r units, is **

(A) r^{2}/4 sq units

(B) 2r^{2} sq.units

(C) r^{2} sq.units

(D) r^{2}/2sq units

**Answer**

C

**Question. If a chord of a circle of radius 28 cm makes an angle of 900at the centre, then the area of the major segment is **

(A) 392 cm^{2}

(B) 1456 cm^{2}

(C) 1848 cm^{2}

(D) 2240 cm^{2}

**Answer**

A

**Question. If area of a circle inscribed in an equilateral triangle is 48π square units, Then perimeter of the triangle is **

(A) 17√3units

(B) 36 units

(C) 72 units

(D) 48√3

**Answer**

D

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

(A) > r

^{2}

(B) =r

^{2}

(C) < r

^{2}

(D) None of these

**Answer**

B

**Question. The area of a circular path of uniform width h surrounding a circular region of radius r is **

(A) π(2r + h)r

(B) π(2r + h)h

(C) π (h + r)r

(D) π(h + r)h

**Answer**

B

**Question. Area of the largest triangle that can be inscribed in a semi –circle of radius r units is **

(A) r^{2}sq. units

(B) 1/2 r^{2}sq. units

(C) 2r^{2}sq. units

(D) √2r^{2}sq. units

**Answer**

A

**PRACTICE EXERCISE**

**Question. The outer circumference of a circular racing track is 220 m. The track is everywhere 7 m wide. Calculate the cost of levelling the track at the rate of 50 paisa per sq. m.[use π = 22/7]****Solution.** Rs. 693

**Question. A bicycle wheel makes 5,000 revolutions in moving 11 km. Find the diameter of the wheel.****Solution.** 70 cm

**Question. Find the area of the sector of a circle whose radius is 14 cm and angle of sector is 45°.****Solution.** 77 cm^{2}

**Question. A copper wire, when bent in the form of a square, encloses an area of 484 cm2. If the same wire is bent in the form of a circle, find the area enclosed by it. [take π = 22/7]****Solution. **616 cm^{2}

**Question. An arc of length 20 π cm subtends an angle of 144° at the centre of the circle. Find the radius of the circle.****Solution.** 25 cm

**Question. A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm ^{2} . If the same wire is bent in the form of a circle, find the area of the circle.**

**Solution.**346.5 cm

^{2}

**Question. A sector of a circle of radius 8 cm contains an angle of 135°. Find the area of the sector.****Solution.** 24 π cm^{2}

**Question. The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.****Solution.** 45.03 m^{2}

**Question. In the given figure, O is the centre of the circle of radius 9 cm and ∠AOB = 150°. Find : (i) the length of the major arc**

**(ii) the area of the major sector. [use π = 22/7]**

**Solution.** (i) 33 cm (ii) 148.5 cm^{2}

**Question. An arc of a circle of radius 21 cm has a length of 17.6 cm. Find the angle subtended at the centre of the circle.****Solution. **48°

**Question. In the given figure, the length of the minor arc is (7/24) of the circumference of the circle. Find : ****(i) ∠AOB****(ii) If it is given that the circumference of the circle is 132 cm, find the length of the minor arc AB and the radius of the circle.**

**Solution.** (i) 105° (ii) 38.5 cm, 21 cm

**Question. Find the area of a segment of a circle of radius 7 cm if the arc of the segment has measure 90°.****Solution.** 14 cm^{2}

**Question. In the given figure, there are shown sectors of two concentric circles of radii 7 cm and 3.5 cm. Find the area of the shaded region. [use π = 22/7] **

**Solution.** 9.625 cm^{2}

**Question. The given figure shows a quadrant of a circle of radius 10 cm. Find the area of the shaded region and the perimeter of the sector. **

**Solution.** 28.57 cm^{2}, 35.71 cm

**Question. The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/hr?****Solution.** 250

**Question. Find the area of the segment of a circle, given that the angle of the sector is 120° and the radius of the circle is 21 cm. [Take π = 22/7 and √3 = 1.73]****Solution.** 271.2675 cm^{2}

**Question. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find :****(i) Area of the minor sector****(ii) Area of the minor segment****(iii) Area of major sector****(iv) Area of major segment [use π = 3.14]****Solution.** (i) 78.5 cm^{2} (ii) 28.5 cm^{2} (iii) 235.5 cm^{2} (iv) 285.5 cm^{2}

**Question. The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 9:00 am and 9:35 am.****Solution.** 183.3 cm^{2}

**Question. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. [use π = 3.14, √3 = 1.73]****Solution.** 88.44 cm^{2}

**Question. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.****Solution.** 1254.96 cm^{2}

**Question. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. [use π = 3.14]****Solution.** 189.97 km^{2}

**Question. The area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.****Solution.** 14 cm

**Question. A square is inscribed in a circle of radius 10 cm. Find the area of the circle, not included in the square [use π = 3.14]****Solution.** 114 cm^{2}

**Question. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first?****Solution.** 132 m

**Question. A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road. [use π = 22/7]****Solution.** 2618 m^{2}

**Question. In the given figure, ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region. 35****Solution.** (16 π – 12 √3 ) cm^{2}

**Question. The side of a square is 42 cm. Find the area of (i) the inscribed circle (ii) the circumscribed circle.****Solution.** (i) 1386 cm2 (ii) 2772 cm^{2}

**Question. The following figure shows a rectangle ABCD inscribed in a circle. ****(i) If AB = 8 cm and BC = 6 cm, find the area of the circle not included in the rectangle.****(ii) If diameter of the circle is 25 cm and BC = 15 cm, find the area of the circle not included in the given rectangle.**

**Solution.** (i) 30.55 cm^{2} (ii) 190.635 cm^{2}

**Question. A wheel of diameter 42 cm, makes 240 revolutions per minute. Find :****(i) the total distance covered by the wheel in one minute.****(ii) the speed of the wheel in km/hr.****Solution.** (i) 316.8 m (ii) 19.008 km/hr

**Question. Find the area of a quadrant of a circle whose circumference is 22 cm.****Solution.** 9.625 cm^{2}

**Question. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal, semi-circles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of the shaded region. **

**Solution.** 12 π cm, 37.71 cm^{2}

**Question. A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi-circular portion with BC as diameter is cut off. Find the area of the remaining part.****Solution.** 203 cm^{2}

**Question. In the given figure, ABCD is a square. AEB and DFC are arcs of a circle whose centre is the centre of the square. If the area of the square is 49 cm2, find the area of the shaded region. **

**Solution.** 14 cm^{2}

**Question. Four equal circles are described about the four corners of a square so that each touches two of the others as shown in figure. Find the area of the shaded region, if each side of the square is 14 cm. **

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

**Question. Find the area of the circle whose circumference is 22 cm.****Solution.** 38.5 cm^{2}

**Question. A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form. Find the length of the side of the square.****Solution.** 44 cm

**Question. A race track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. Find the width of the track.****Solution.** 7 m

**Question. Find the area of the shaded parts in the following figures, all dimensions being in cm. **

**Solution.** (i) 672 cm^{2} (ii) 19.3 cm^{2} (iii) 462 cm^{2} (iv) 2328 , 2/7cm^{2}

(v) 14.3 cm^{2} (vi) 192.5 cm^{2} (vii) 231 cm^{2} (viii) 336 cm^{2}

(ix) 231 cm^{2} (x) 378 cm^{2}

**Question. ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is drawn as shown in figure. Find the area of the shaded portion. **

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

**Question. In the following figure, ABC is an equilateral triangle. Circles are drawn with vertices of the triangle ABC as centres so that every circle touches the remaining two. If the perimeter of the triangle ABC is 84 cm. Find ****(i) area of sector, inside the triangle, of each circle.****(ii) area of the triangle which is not included in the circle. [use π = 3.14, √3 = 1.73]**

**Solution.** (i) 102.57 cm2 (ii) 31.37 cm^{2}

**Question. In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. **

**Solution.** 66.5 cm^{2}

**Question. In the given figure, find the area of the shaded region, where ABCD is a square of side 10 cm. [use π = 3.14]. **

**Solution.** 57 cm^{2}

**Question. Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another (see figure). What area will be left ungrazed? **

**Solution.** 535.71 m^{2}

**Question. In the given figure, diameter of the biggest semi-circle is 108 cm, and diameter of the smallest circle is 36 cm, calculate the area of the shaded region. **

**Solution.** 1272.86 cm^{2}

**Question. Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area, enclosed between the circles is 24/7 cm ^{2} . Find the radius of the each circle. **

**Solution.** 2 cm

**Question. The given figure shows a square OABC, inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. **

**Solution.** 228.57 cm^{2}

**Question. Three horses are tethered with 7 m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed.****Solution.** 77 m2, 259 m^{2}

**Question. In an equilateral triangle of side 12 cm, a circle is inscribed touching its sides. Find the area of the portion of the triangle not included in the circle. [use √3 =1.73 and π = 3.14]****Solution.** 24.6 cm^{2}

**Question. In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find the area of the shaded region. **

**Solution.** 770 cm^{2}

**Question. In the given figure, ABCD is a rectangle with sides 4 cm and 8 cm. Taking 8 cm as the diameter, two semicircles are drawn. Find the area overlapped by the two semi-circles. **

**Solution.** 19.66 cm^{2}

**Question. A circle has been inscribed in a square of side 4 cm. Determine the left out area. What will be the left out area of the circle if a square is inscribed in the circle? [use π = 3.14]****Solution.** 3.44 cm^{2}; 4.56 cm^{2}

**Question. Find the radius of a circle whose area is equal to the sum of the areas of the three circles whose radii are 3 cm, 4 cm, and 12 cm.****Solution.** 13 cm

**Question. Find the area of the shaded region shown in the figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. **

**Solution.** (660/7 + 36√3)cm^{2}

**Question. In the given figure, there are three semi-circles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm. Calculate : ****(i) the area of the shaded region.****(ii) the cost of painting the shaded region at the rate of 50 paisa per cm ^{2}, to the nearest Rs.**

**Solution.** (i) 12.375 cm^{2} (ii) Rs. 6

**Question. Two circles touch externally. The sum of their areas is 130 π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.****Solution.** 11 cm and 3 cm

**Question. Find the perimeter and area of the shaded region whose particulars are given below in each of the following : **

**Solution.** (i) 88 cm, 154 cm^{2} (ii) 44 cm, 42 cm^{2} (iii) 176 cm, 1232 cm^{2} (iv) 34 cm, 61.5 cm^{2}

(v) 32.6 cm, 29.7 cm^{2} (vi) 31.4 cm, 57.1 cm^{2} (vii) 58.9 cm, 225 cm^{2} (viii) 189 cm, 1697 cm^{2}

(ix) 50.3 cm, 116 cm^{2 }(x) 37.8 cm, 42.6 cm^{2}

**Question. A garden roller has a circumference of 3 m. How many revolutions does it make in moving 21 m?****Solution.** 7

**Question. In the given figure, a piece of cardboard is given in the shape of a trapezium ABCD where AB || DC and ∠BCD = 90°. A quarter circle BFEC is removed from the cardboard. Given AB = BC = 3.5 cm and DE = 1.5 cm. Calculate the area of the remaining piece of the cardboard. **

**Solution.** 5.25 cm^{2}

**Question. A square park has each side of 100 m. At each corner of the park, there is a flower bed in the form of a quadrant of radius 14 m as shown. Find the area of the remaining part of the park. [use π = 22/7] **

**Solution.** 9384 m^{2}

**Question. An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. **

**Solution.** 795.54 cm^{2}

## Mathematics Areas Related To Circles Worksheets for Class 10 as per CBSE NCERT pattern

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