Q.No.2: Find the radius of the circle in which a central angle of 60° intercepts an arc of length 37.4 cm (use n = 22/7).
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Answers
Answer:
q1
Given,
Length of the arc = l = 37.4 cm
Central angle = θ = 60° = 60π/180 radian = π/3 radians
We know that,
r = l/θ
= (37.4) * (π / 3)
= (37.4) / [22 / 7 * 3]
= 35.7 cm
Hence, the radius of the circle is 35.7 cm.
q2
Given,
Number of revolutions made by the wheel in 1 minute = 360
1 minute = 60 seconds
Number of revolutions in 1 second = 360/60 = 6
Angle made in 1 revolution = 360°
Angles made in 6 revolutions = 6 × 360°
Radian measure of the angle in 6 revolutions = 6 × 360 × π/180
= 6 × 2 × π
= 12π
Hence, the wheel turns 12π radians in one second.
hope it helps you
Solution:
Answer1
Given,
Length of the arc = l = 37.4 cm
Central angle = θ = 60° = 60π/180 radian = π/3 radians
We know that,
r = l/θ
= (37.4) * (π / 3)
= (37.4) / [22 / 7 * 3]
= 35.7 cm
Hence, the radius of the circle is 35.7 cm.
Answer2:--
Given,
Number of revolutions made by the wheel in 1 minute = 360
1 minute = 60 seconds
Number of revolutions in 1 second = 360/60 = 6
Angle made in 1 revolution = 360°
Angles made in 6 revolutions = 6 × 360°
Radian measure of the angle in 6 revolutions = 6 × 360 × π/180
= 6 × 2 × π
= 12π
Hence, the wheel turns 12π radians in one second.