Respuesta :

Answer:

6.6 cm and 14.6 cm

Step-by-step explanation:

(a)

the length of arc AB is calculated as

AB = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{95}{360}[/tex]

     = 2π × 4 × [tex]\frac{95}{360}[/tex]

     = 8π × [tex]\frac{95}{360}[/tex]

     = [tex]\frac{8\pi (95)}{360}[/tex]

     ≈ 6.6 cm ( to the nearest tenth )

(b)

the perimeter (P) of sector AOB is

P = r + r + AB = 4 + 4 + 6.6 = 14.6 cm

reinhard10158

Step-by-step explanation:

3.

the circumference of a circle is

2×pi×r

r = 4 cm

so, we know, the full circle circumference is

2×pi×4 = 8×pi = 25.13274123... cm

a.

the arc length of AB is the part of the whole circumference that corresponds to 95° out of the full 360° of a whole circle.

arc AB = 8×pi × 95/360 = pi × 95/45 = pi × 19/9 =

= 6.632251158... cm

b.

the perimeter of OAB (the "pie slice") is then the arc AB plus 2 radius lengths (from the end points on the arc to the center of the circle) :

pi × 19/9 + 2×4 = pi×19/9 + 8 = 14.632251158... cm

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