Q.- The inner circumference of a circular track is 220 m. The track is 7m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of j- 2 per metre. (Use π = 22/7)
Sol. Let the inner and outer radii of the circular
track be r metres and R metres respectively.
Then,
Inner circumference = 220 metres
= 2πr = 220
=2 × 22/7 × r = 220
=r = 35 m
Since the track is 7 metre wide everywhere.
Therefore,
R = Outer radius = r + 7 = (35 + 7) m = 42 m
Outer circumference
= 2πR = 2 × 22/7 × 42 m = 264 m
Rate of fencing = j- 2 per metre
Q.- A bicycle whell makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.
Sol. Let the radius of the wheel be r cm.
Distance covered by the wheel in one revolution
Distance moved /Number of revolutions = 11/5000 km
11/5000 × 1000 × 100 cm = 220 cm
Circumference of the wheel = 220 cm
=2πr = 220 cm
2 × 22/7 × r = 220
= r = 35 cm
Diameter = 2r cm = (2× 35) cm = 70 cm
Hence, the diameter of the wheel is 70 cm.
AREAS RELATED TO CIRCLES
SECTION A:
1. If area of a circle is numerically double its perimeter, then find the radius of the circle. (CBSE 2011) (4 units)
2. If the area of a sector is 5/18 of the area of the circle, find the angle subtended by the sector at the centre. (100⁰)
SECTION B:
3. A square is inscribed in a circle. What is the ratio of the areas of the circle and the square. (π : 2)
4. The area enclosed between the two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Find the radius of the outer circle. (CBSE 2011) (17.5 cm)
5. If r and R are the respective radii of the smaller and bigger semi-circles, find the area of the shaded portion. ( CBSE 2010) (πR2)
SECTION C:
6. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) (954.56cm)
7. OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. Find the area of the rhombus, if the area of the circle is 1256 cm2. (Use π = 3.14) (20000√3cm2)
8. ABCD is a field in the shape of a trapezium with AD ‖ BC, ∠ABC = 90⁰ and ∠ADC = 60⁰. Four sectors are formed with centres A, B, C and D. The radius at each sector is 14 m. Find the total area of four sectors. (CBSE 2012) (616 m2)
SECTION D:
9. 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. (CBSE 2013) (280)
10. In fig.3, AOB is a quarter circle. OCB and OCA are semicircles with OB and OA as diameters where ar(OCO) = a sq. units and ar(BCAB) = b sq. units. Find the relation between a and b. (a = b)
11. In fig.6, ΔABC is right angled at B. AB = 14 cm and BC = 24 cm. With the vertices A,B and C as centres , arcs are drawn of equal radius. Find the area of shaded region. (91 cm2)
(91
More MCQs for NCERT Class 10 Mathematics Area Related To Circle....
1. 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)
2. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is
(A) 50 √2cm
(B) 100 πcm
(C) 50√2cm
(D) 100√2 cm
Answer : (C)
3. 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)
4. 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)
5. 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)
6. 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 r21 + r22
(A) > r2
(B) = r2
(C) 2
(D) None of these
7. 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)
8. 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 cm2
(B) 3π/3 cm2
(C) 25π cm2
(D) 25π/3 cm2
Answer : (D)
9. 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)
10. 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)
11. 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)
12. 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)
13. The area of a sector whose perimeter is four times its radius r units, is
(A) r2/4 sq units
(B) 2r2 sq.units
(C) r2 sq.units
(D) r2/2 sq units
Answer : (C)
14. 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 cm2
(B) 1456 cm2
(C) 1848 cm2
(D) 2240 cm2
Answer : (A)
15. 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)
16.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 √1)cm2
(B) 2 4( 3 √1)cm
(C) 2 6( 3 √1)cm
(D) 2 8( 3 √1)cm
Answer : (B)
17. 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)
18. Area of the largest triangle that can be inscribed in a semi –circle of radius r units is
(A) r2sq. units
(B) 1/2 r2 sq units
(C) 2r2 sq.units
(D) √2r2 sq.units
Answer : (A)
19. 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
(A) r = r1 + r2
(B) r12 + r22 =r2
(C) r1 + r2 < r
(D) r12 + r22 < r2
Answer : (B)
20. If the sum of the circumferences of two circles with radii r1 + r2 is equal to the circumference of a circle of radius r, then
(A) r = r1 + r2
(B) r1 + r2 > r
(C) r1 + r2 < r
(D) None of these
Answer : (A)
Please click on below link to download CBSE Class 10 Mathematics Area Related To Circle Worksheet Set C
