question_answer

In a circle of radius 28 cm, an arc subtends an angle of \[45{}^\circ \]at the centre. Then, the length of the arc and the area of the sector is

A) \[44\text{ }cm,\text{ }154\text{ }c{{m}^{2}}\]

B) \[22cm,154\text{ }c{{m}^{2}}\]

C) \[22cm,308\text{ }c{{m}^{2}}\]

D) None of these

Correct Answer: C

Solution :

Given, r = 28 cm and \[\theta =45{}^\circ \] \[\therefore \]Arc length \[=\frac{\theta }{360{}^\circ }\times 2\pi r\] \[=\frac{45{}^\circ }{360{}^\circ }\times 2\times \frac{22}{7}\times 28\] \[=\frac{1}{8}\times 2\times 22\times 4=22\,cm\] Now, area of sector \[=\frac{1}{2}\times l\times r\] [where, l = arc length] \[=\frac{1}{2}\times 22\times 28\] \[=22\times 14\text{ }=308\text{ }c{{m}^{2}}\]