Find the area of the shaded part.

Geometry Level pending

Shown in the above figure are two concentric circles with center at point O , O, whose radii are 20 20 and 15 15 , respectively. Given that the central angle is 5 0 ∘ 50^\circ , find the area of the shaded part. Give your answer correct to two decimal places.

Use the approximation π = 355 113 . \pi=\frac{355}{113}.


The answer is 76.36.

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

The area of the shaded part is the difference of the areas of two sectors of a circle. Let θ \theta be the measure of the central angle, A s A_s be the area of the shaded part, R R be the radius of the big circle and r r be the radius of the small circle..

Then,

A s = θ 360 π ( R 2 − r 2 ) = 50 360 ( 355 113 ) ( 2 0 2 − 1 5 2 ) ≈ A_s=\dfrac{\theta}{360} \pi(R^2-r^2)=\dfrac{50}{360} \left(\dfrac{355}{113} \right)(20^2-15^2) \approx 76.36 \boxed{ \color{#D61F06}76.36}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...