What is the length of an arc of a circle that subtends 2 1/2 radians at the centre when the radius of the circle is 8cm
there are 2 pi radians in a circle
C = 2 pi R
so
(2.5/2pi)(2 pi R)
= 2.5 R
= 2.5 * 8 = 20
or, just remember that
s = rθ = 5/2 * 8 = 20
Well, well, well, isn't geometry just a circle of fun! To find the length of an arc, you need to use a little formula: arc length = radius times the angle in radians. So, in this case, the angle is 2 1/2 radians and the radius is 8 cm. Time for a little math magic: 2.5 times 8 gives us 20 cm. Voila! The length of the arc is 20 cm, and now you can go forth and spread your geometric genius!
To find the length of an arc of a circle, you can use the formula:
Arc Length = Radius × Central Angle
Given that the radius of the circle is 8 cm and the central angle is 2 1/2 radians, we can substitute these values into the formula:
Arc Length = 8 cm × 2 1/2 radians
First, let's convert the mixed fraction to a decimal:
2 1/2 = 2 + 1/2 = 2.5
Now we can calculate the arc length:
Arc Length = 8 cm × 2.5 radians
Arc Length = 20 cm × radians
So, the length of the arc of the circle is 20 cm x radians, or simply 20 radians.
To find the length of an arc of a circle, you can use the formula:
Arc Length = (θ/360) * 2πr
Where:
- θ is the central angle in radians
- r is the radius of the circle
In this case, the central angle θ is given as 2 1/2 radians, and the radius r is given as 8 cm. We need to convert 2 1/2 radians to a decimal value.
To convert 2 1/2 radians to a decimal, we need to express the fraction as a decimal. To do this, divide the numerator, 5, by the denominator, 2:
5 ÷ 2 = 2.5
Therefore, 2 1/2 radians is equal to 2.5 radians.
Now, we can substitute the values into the formula:
Arc Length = (2.5/360) * 2π * 8
Simplify the formula:
Arc Length = (2.5/360) * 16π
Now, you can calculate the length of the arc by multiplying (2.5/360) by 16π:
Arc Length ≈ (2.5/360) * 16π ≈ 0.044167 * 16π ≈ 0.70667π
So, the length of the arc is approximately 0.70667π cm.