Step by step solution to "ind the area of the shaded region. Round..."

High School
Geometry
High school geometry
Circles

Cassidy Johnson

Answered question

2022-02-13

ind the area of the shaded region. Round to 2 decimal places.

Answer & Explanation

Kaylie Carroll

Beginner2022-02-14Added 12 answers

Step 1
Given, two concentric circles.
Let the radius of the outer circle

= r_{1} = 25 c m

and the radius of the inner circle

= r_{2} = 15 c m

The task is to find the area of the region between these two circles.
Step 2
Find the areas of the two circles and subtract it to get the area of the shaded region.
The area of the outer circle

= 2 π {(r_{1})}^{2} c m^{2}

= 2 π {(25)}^{2} c m^{2}

= 1250 π c m^{2}

The area of the inner circle

= 2 π {(r_{2})}^{2} c m^{2}

= 2 π {(15)}^{2} c m^{2}

= 450 π c m^{2}

The required area

= (2 π r_{1} - 2 π r_{2}) c m^{2}

= 2 π (1250 - 450) c m^{2}

= 800 π c m^{2}

\approx 2513.27 c m^{2}

Therefore, the shaded area is

2513.27 c m^{2}

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