Question

In the following figure, the area of the shaded region is $20$% of the area of the whole circle centered at P. The angle shown measures d degrees. What is its measurement in radians?

• A. $\frac{1}{5}\pi$
• B. $\frac{2}{5}\pi$
• C. $\frac{4}{5}\pi$
• D. $\frac{2}{15}\pi$
• E. $\frac{4}{15}\pi$

Answer 1

Answer: (B)

$\frac{2}{5}\pi$

Since the shaded region occupies $20$ % of the whole circle, it occupies $\frac{1}{5}$ of the circle.
We know that ${360}^0$ or $2\pi$ is the angle within one full circle.
Hence, angle $d^0=\frac{1}{5}\times 2\pi =\frac{2\pi }{5}$