Question

A circle has a sector with area \dfrac{64}{5}\pi 5 64 ​ πstart fraction, 64, divided by, 5, end fraction, pi and central angle of \purple{\dfrac{8}{5}\pi} 5 8 ​ πstart color #9d38bd, start fraction, 8, divided by, 5, end fraction, pi, end color #9d38bd radians . What is the area of the circle?

Answer 1

Answer:

Area of circle is $\dfrac{1024\:\pi}{25}$

Step-by-step explanation:

Since angle $\theta$ is given in radians, so using formula for area of sector in radians is given as,

$Area\:of\:sector=\dfrac{1}{2}\:r^{2}\:\theta$

Given area of sector and angle. Therefore substituting the values in above formula,

$\dfrac{64\pi}{5}=\dfrac{1}{2}\:r^{2}\:\left (\dfrac{8\pi}{5}\right )$

Cancelling out the common term,

$16=\dfrac{1}{2}\:r^{2}$

Multiplying with 2 on both sides,

$16=r^{2}$

Therefore value of $r^{2}$ is $16$

Formula for area of circle is,

$Area\:of\:circle=\pi\:r^{2}$

Substituting the value,

$Area\:of\:circle=\pi\times16$

$Area\:of\:circle=16\pi$

Therefore area of circle is $16\pi$