Question

What is the area,in square centimeters,of a circle that has a circumference of 16 centimeters?

Answer 1

Answer: $20.38\ cm^2$

Step-by-step explanation:

We know that the circumference of a circle is given by :-

$C=2\pi r$, where r is the radius of the circle .

Given : Circumference of circle = 16 cm

Then, $16=2\pi r$

i.e $r=\dfrac{16}{2\pi}=\dfrac{8}{\pi}$          (1)

We know that the area of circle is given by :-

$A=\pi r^2$

i.e. $A=\pi (\dfrac{8}{\pi})^2$                    [From (1)]

i.e. $A=\pi (\dfrac{64}{\pi^2})$

i.e. $A=\dfrac{64}{\pi}$

Put $\pi=3.14$

$A=\dfrac{64}{3.14}=20.3821656051approx20.38\ cm^2$

Hence, area of circle = $20.38\ cm^2$