In the diagram below, the angle between the two radii is $45^\circ$. The radius of the circle is $4cm$. What is the length of the arc and area of the shaded sector?

Substitute $r=4$ and $\theta=45$ into both equations:

$\text{Arc\,length}=\frac{\theta}{360}\times2\pi r =\frac{45}{360}\times2\times\pi\times4$

The sector of a circle is a portion of the circle that is bounded by two radii.

What is the formula for the area of a circle?

The formula for the area of a circle is πr^2, where r is the radius.

What is the circumference of a circle?

The circumference is the name given to the perimeter of the circle. The formula to calculate it is 2πr or πd, where r is the radius and d is the diameter.