Question

the formula below gives the area of a semi-circle, \\(a\\), with a radius of \\(r\\).

\\a = \frac{1}{2}\pi r^2\\

solve the formula for the radius.

\\(r = \frac{1}{2}\sqrt{\frac{\pi}{a}}\\)

\\(r = \sqrt{\frac{\pi}{2a}}\\)

\\(r = 2\sqrt{\frac{a}{\pi}}\\)

\\(r = \sqrt{\frac{2a}{\pi}}\\)

Explanation:

Isolate the term containing r

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Divide by pi

$$ r^2 = \frac{2A}{\pi} $$

Take the square root

$$ r = \sqrt{\frac{2A}{\pi}} $$

Answer:

• (A) \(r = \frac{1}{2}\sqrt{\frac{\pi}{A}}\)
• (B) \(r = \sqrt{\frac{\pi}{2A}}\)
• (C) \(r = 2\sqrt{\frac{A}{\pi}}\)
• (D) \(r = \sqrt{\frac{2A}{\pi}}\) (Correct answer)