Question

A circle has an area of 36pi square inches. Find its radius, diameter and exact circumference

Answer 1

we use the formula of the area

$A=\pi\times r^2$

where A is the area and r the radious

Radious

we can replace the value of the area and solve for r

$\begin{gathered} 36\pi=\pi\times r^2 \\ \\ r^2=\frac{36\pi}{\pi} \\ \\ r^2=36 \\ r=6 \end{gathered}$

Value of the radious is 6inches

Diameter

diameter is twice radious

$\begin{gathered} d=6\times2 \\ d=12 \end{gathered}$

Value of the diamter is 12 inches

Circumference

we use the formula of the periemter

$P=2\pi\times r$

and replace the value of radious

$\begin{gathered} P=2\pi\times6 \\ P=12\pi \end{gathered}$

Value of the circumference is 12pi inches