MathRevolution wrote:
Attachment:
8.2.png
There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is \(14π\). What is the area of the small circle?
\(A. 3π\)
\(B. 3.5π\)
\(C. 4π\)
\(D. 4.5π\)
\(E. 7π\)
Given Area of big circle \(= 14π\)
Let the radius of big circle be \(= R\)
\(\pi\)\(R^2 = 14π\)
\(R^2 = 14\)
\(R = \sqrt{14}\)
Given diameter of small circle is equal to radius of big circle.
Let the radius of small circle be \(= r\)
Therefore \(R = 2r\)
\(r = \frac{R}{2}\) \(= \frac{\sqrt{14}}{ 2}\)
Area of small circle \(= \pi r^2 = \pi * \frac{\sqrt{14}}{ 2} * \frac{\sqrt{14}}{ 2} = \pi * \frac{14}{4} = \frac{7}{2} \pi = 3.5\pi\)
Answer (B)..._________________
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