Question

given circles v and w below. find the area of the shaded region. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Find the radius of circle \( W \)

The diameter of circle \( W \) is \( 18 \), so the radius \( r_W=\frac{18}{2} = 9 \)

Step2: Find the radius of circle \( V \)

The radius of circle \( V \) \( r_V\) is twice the radius of circle \( W\), so \( r_V = 18 \)

Step3: Calculate the area of circle \( V \)

The area formula of a circle is \( A=\pi r^{2} \). For circle \( V \), \( A_V=\pi\times18^{2}=324\pi \)

Step4: Calculate the area of circle \( W \)

For circle \( W \), \( A_W=\pi\times9^{2} = 81\pi \)

Step5: Calculate the area of the shaded region

The area of the shaded region \( A = A_V - A_W\)

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Answer:

\(763.0\)