Question

r=15cm, central angle=45° find the length of the arc, area of the sector and perimeter of the sector?​

Answer 1

Answer:

area=88.39 , perimeter of sector =11.78

Answer 2

Answer:

The length of of the arc is 11.775 cm.

Area of the sector is 88.3125 cm².

Perimeter of the sector is 41.775 cm.

Step-by-step explanation:

Radius of the circle = 15cm

Central angle subtended by the given arc = 45°

Perimeter of the circle = $2\pi r$

                                     = 2 × 3.14 × 15

                                     = 94.2 cm

Length of the arc = $\frac{central angle}{360}$ × perimeter

                            =  $\dfrac{45^{\circ }}{360^{\circ }}\times 94.2$

                            = 11.775 cm

Area of the circle = $\pi r^{2}$

                             = 3.14 × 15²

                             = 706.5 cm²

Area of the sector = $\frac{central angle}{360}$ × area

                              = $\dfrac{45^{\circ }}{360^{\circ }}\times 706.5$

                              = 88.3125 cm²

Perimeter of the sector = length of the arc + 2 × radius

                                       = 11.775 + 2 × 15

                                       = 41.775 cm