A piece of wire is in form of an arc of a circle,radius 10.5.Find the length of the wire given that the angle at the center of the arc is 150°?

To find the length of the wire, we need to calculate the circumference of the circle formed by the arc.

The formula for the circumference of a circle is:
C = 2πr

Given that the radius of the circle is 10.5, we can substitute this value into the formula:
C = 2π(10.5)
C = 21π

Now, we need to find the length of the arc which is a fraction of the circumference based on the angle at the center of the arc.

The formula for the length of an arc is:
L = (θ/360) * C

Where θ is the angle at the center of the arc and C is the circumference of the circle.

Given that the angle at the center of the arc is 150°, we can substitute this value into the formula:
L = (150/360) * 21π
L = (5/12) * 21π
L = 35π/12

Therefore, the length of the wire in the form of an arc of a circle with a radius of 10.5 and an angle at the center of 150° is 35π/12 units.

The length of the wire $s$ is given by the formula
$$s=r\theta$$

Where $$r=10.5,\theta=\frac{150\pi}{180}=\frac{5\pi}{6}$$

Substituting the values into the formula, we get:
$$s=10.5(\frac{5\pi}{6})$$ $$s=27.92\approx28$$

Therefore,the length of the wire is approximately 28 units.