Question

What is the perimeter of a quadrant of a circle with radius $3cm$?

Answer 1

Determine the perimeter of the quadrant of the circle.

The quadrant of a circle includes one-fourth of the circumference of the circle and two lengths that are equal to the radius.

Use the formula $C=2\pi r$ and the length of the radius $r=3\mathrm{cm}$ to determine the perimeter:

$\begin{array}{rcl}P& =& \frac{2\pi \times 3}{4}\mathrm{cm}+3\mathrm{cm}+3\mathrm{cm}\\ & \Rightarrow & P=1.5\pi +6\mathrm{cm}\end{array}$

Hence, the perimeter of the quadrant is $\begin{array}{rcl}& & 1.5\pi +6\mathrm{cm}\end{array}$.