Answer:

51.95cm^2

Step-by-step explanation:

Area of arc=(angle/360)*pi*r^2

=(150/360)*22/7*6.3^2

=51.95cm^2

Given:

In the circle radius is 6.3cm

An arc subtends of angle measure 150°  

To find:

1. To find the length of the given arc.
2. The area of the sector formed by this arc.

Solution:

The radius of circle = 6.3cm

The angle of the arc = 150°

Length of the arc = Ф°/360° × (2πr)

Now, we will put the values and find the values

1. Length of the arc = Ф°/360° × (2πr)

                             = 150/360 × 2 × [tex]\frac{22}{7}[/tex] × 6.3

                             = [tex]\frac{5}{12}[/tex] × 2 × [tex]\frac{22}{7}[/tex] × 6.3

                             =  16.5cm

Length of the arc = 17cm (approx)

2. Area of the sector formed by the arc.  

Area of sector = Ф°/360° × πr²

                        = 150/360 ×[tex]\frac{22}{7}[/tex] × 6.3 × 6.3

                        = [tex]\frac{5}{12}[/tex] × [tex]\frac{22}{7}[/tex] × 6.3 × 6.3  

                        =  51.97cm²  

Area of the sector = 52cm²(approx)

Area of the sector formed by arc is 52cm².

Length of the arc = 17cm .

Area of the sector formed by arc is 52cm².