Question

The circumference of a circle is 18TT inches. Which choice represents the exact area. of the circle? A: $81\pi \: {inches}^{2}$ B: $324\pi \: {inches}^{2}$C: $254.34 \: {inches}^{2}$D: $1017.36 \: {inches}^{2}$

Answer 1

the circumference of the circle is,

2 x pi x r = 18 x pi

r = 18/2

r = 9

so the radius of the circle is 9

we know that the area of the circle is,

$A=\pi\times r^2$

put the value r = 9

$\begin{gathered} A=\pi\times9^2 \\ A=81\times\pi \end{gathered}$

the area of the circle is 81 pi

thus the answer is option A