find the length of an arc of a circle of radius 5.6 cm which subtends an angle of 60 degrees at the centre of the circle.(take pie as 22 divided by 7.)
this text book doesn't explain what the question is all about
To find the length of an arc of a circle, you can use the formula:
Arc Length = (θ/360) x 2πr
Where:
θ = the angle subtended by the arc
r = the radius of the circle
In this case, the radius is 5.6 cm and the angle is 60 degrees. Plugging these values into the formula, we have:
Arc Length = (60/360) x 2 x (22/7) x 5.6
Calculating this, we get:
Arc Length = (1/6) x 2 x (22/7) x 5.6
Arc Length = (1/3) x (22/7) x 5.6
Arc Length = (22/21) x 5.6
Simplifying this further:
Arc Length = 22 x 5.6 / 21
Arc Length = 123.2 / 21
Arc Length ≈ 5.867 cm
Therefore, the length of the arc of a circle with a radius of 5.6 cm and subtending an angle of 60 degrees at the center is approximately 5.867 cm.
To find the length of an arc of a circle, you need to use the formula:
Arc Length = (θ/360) * 2πr
Where:
- θ is the central angle in degrees
- r is the radius of the circle
In this case, the radius is given as 5.6 cm, and the central angle is 60 degrees. Also, π can be approximated as 22/7.
Let's substitute these values into the formula:
Arc Length = (60/360) * 2 * (22/7) * 5.6 cm
Simplifying further:
Arc Length = (1/6) * (2 * 22/7) * 5.6 cm
Arc Length = (1/6) * (44/7) * 5.6 cm
Arc Length = (1/6) * (44/1) cm
Arc Length = 44/6 cm
The length of the arc is approximately 7.33 cm.
arc = rØ, where Ø is the central angle in radians, so
arc = 5.6(π/3) = appr 5.86 cm
or
use a ratio:
circumference = 2πr = 11.2π
arc/11.2π = 60/360
arc = 11.2π(1/6) = 5.6π/3 = appr 5.86 cm
btw, with every calculator these days having a π key, nobody uses 22/7 or π anymore.
How old is your textbook?