In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find:
(i)the circumference of the circle
(ii)the area of the circle
(iii)the length of the arc AB,
(iv)the area of the sector OAB.
Answers
Answer:
The circumference of a circle is 37.71 cm , Area of a circle is 113.1 cm² , Length of an arc, AB 11.52 cm and Area of sector of a circle,AOB is 34.5 cm²
Step-by-step explanation:
Given :
Radius of circle, r = 6 cm
Chord of a circle = 10
Angle at the centre of the circle, θ = 110°
(i) Circumference of a circle ,C = 2πr
C = 2 × 22/7 × 6
C = 264/7
C = 37.71 cm
Circumference of a circle = 37.71 cm
(ii) Area of a circle,A = πr²
A = 22/7 × 6²
A = 22/7 × 36
A = 792/7
A = 113.1 cm²
Area of a circle = 113.1 cm²
(iii) Length of an arc ,l = (θ/360) × 2πr
l = (110°/360°) × 2 × 22/7 × 6
l = 11/36 × 44/7 ×6
l = (11 × 44 ×6) / (36 × 7)
l = 484/ 6×7 = 484/42
l = 11.52 cm
Length of an arc,AB = 11.52 cm
(iv) Area of the sector of a circle, AOB = (θ/360) × πr²
= (110°/360°) × 22/7 ×6²
= 11/36 × 22/7 × 36
= (11 × 22 ) /7
= 242/7
= 34.5 cm²
Area of sector of a Circle ,AOB = 34.5 cm²
Hence, the circumference of a circle is 37.71 cm , Area of a circle is 113.1 cm² , Length of an arc, AB 11.52 cm and Area of sector of a circle,AOB is 34.5 cm²
HOPE THIS ANSWER WILL HELP YOU….
Here are more questions of the same chapter :
AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.
https://brainly.in/question/9458861
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find
(i)the length of the arc
(ii)area of the sector formed by the arc. (Use )
https://brainly.in/question/9458582
Answer:
please verify my ANS were please please please please please please please please and thank my all answer by harshikesh