Question

An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π $c{m}^2$ . The radius of the circle is _______(in cm).

• A. 12
• B. 5
• C. 8
• D. 10

Answer 1

The correct option is C

8

From data,

The area of the sector = $\frac{\theta }{360}$ × $\pi$ × $r^2$ = 20$\pi$ $c{m}^2$

The length of arc = $\frac{\theta }{360}$ × $\pi$ × 2r = 5$\pi$ cm

$\theta$ $r^2$= 7200 and $\theta$r = 900

900 × r = 7200

r = 8 cm.