Arc substend an angle of 45 degree at the centre of a circle of radius 8cm (a)calculate the length of the arc
To calculate the length of an arc, you need to know the angle it subtends at the center of the circle and the radius of the circle. In this case, you have the angle of 45 degrees and the radius of 8 cm.
The formula to calculate the length of an arc is given by:
Length of Arc = (angle in degrees / 360) * (2 * π * radius)
Let's substitute the given values into the formula:
Length of Arc = (45 / 360) * (2 * π * 8)
Simplifying the equation:
Length of Arc = (1/8) * (2 * π * 8)
Now, calculate the length of the arc:
Length of Arc = (1/8) * (16π)
Length of Arc = 2π cm (approximately 6.28 cm)
Therefore, the length of the arc is approximately 6.28 cm.
To calculate the length of the arc, we will use the formula:
Arc Length = (angle/360) x 2πr
Given:
Angle = 45 degrees
Radius = 8 cm
Substituting the values into the formula, we get:
Arc Length = (45/360) x 2π(8)
= (1/8) x 2π(8)
= (1/8) x 16π
= 2π cm
Therefore, the length of the arc is 2π cm.