Solved: "Below are 2 concentric circles, one with a..."

High School
Geometry
High school geometry
Circles

Brooklyn1wp

Answered question

2022-03-02

Below are 2 concentric circles, one with a radius of 5 and the other with a radius of 2. What is the area of the shaded region? Round to 2 decimal places

Answer & Explanation

Nicolle Newman

Beginner2022-03-03Added 4 answers

Step 1
The central angle formed by the sector,

θ = 40^{\circ} = \frac{40 π}{180} = \frac{2 π}{9}

The radius of the smaller and the bigger circles are

r_{1} = 2

and

r_{2} = 5

respectively.
Now, the area of the shaded region can bee valuated as following :
Area

= \frac{1}{2} (r_{1}^{2} - r_{2}^{2}) θ

\Rightarrow Area = \frac{1}{2} \times (5^{2} - 2^{2}) \times \frac{2 π}{9}

\Rightarrow Area = \frac{1}{2} \times 21 \times \frac{2 π}{9}

\Rightarrow Area = \frac{7 π}{3}

\Rightarrow Area \approx 7.33

Required value

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