Question

Find the area of the smaller sector ​

Answer 1

Since the radius is 6 inches, the area is

$A=\pi r^2=36\pi$ squared inches.

Now, the full circle is a sector given by a 360° angle. So, the area of a 140° angle will be proportionate:

$140\div x = 360\div 36\pi$

Solving for $x$, we have

$x=\dfrac{36\pi\cdot 140}{360}=14\pi$