if
ABC is an arc of a circle and angle ABC = 135º, then the ratio of arc ABC to the
circumference is
(a)1:4
(b) 3:4
(c) 3:8
(d) 1:2
Answers
Answer:
3:8
Step-by-step explanation:
The length of an arc subtending an angle ‘
θ
θ’ in a circle of radius ‘r’ is given by the formula,
Length of the arc =
θ
360
°
2
π
r
θ360°2πr
Here, it is given that the arc subtends an angle of 135°with its centre. So the length of the given arc in a circle with radius ‘r’ is given as
Length of the arc =
135
°
360
°
2
π
r
135°360°2πr
The circumference of the same circle with radius ‘r’ is given as
2
π
r
2πr.
The ratio between the lengths of the arc and the circumference of the circle will be,
Lenght of the arc
Cirrumference of the circle
=
135
°
(
2
π
r
)
360
°
(
2
π
r
)
Lenght of the arcCirrumference of the circle=135°(2πr)360°(2πr)
=
135
°
360
°
=135°360°
=
⅜
=3:8