The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 180° arc?
r=4 cm
180°
Give the exact answer in simplest form.

The radius of a circle is 4 centimeters What is the area of a sector bounded by a 180 arc r4 cm 180 Give the exact answer in simplest form class=

Respuesta :

Answer:

8π cm²

Step-by-step explanation:

1. Area of a sector (Degrees)=(Ф/360)*πr²

 Ф= theta

 r=radius

 180/360*π*4²

 1/2*16π

 8π cm²

2. Since the angle is 180°, that means the area is semicircle. The degrees of the whole circle is 360° and half is 180°.

The calculations are still the same.

Area of a semicircle=1/2(πr²)

  1/2 (π*4²)

  16/2 π

  8π cm²

The area of the sector bounded by 180 degree arc is 8[tex]\pi[/tex] cm²

What is a semi-circle?

'A semicircle is a half-circle that is formed by cutting a whole circle into two halves along a diameter line.'

According to the given problem,

Radius of the circle = 4 cm

Area of a semi-circle = [tex]\pi[/tex]r²/2

                                   = ([tex]\pi[/tex] × 4 × 4)/2

                                   = 16[tex]\pi[/tex]/2

                                   = 8[tex]\pi[/tex] cm²

Hence, we can conclude that the area of the sector bounded by the 180 degree arc is 8[tex]\pi[/tex] cm².

Learn more about semi-circle here:

https://brainly.com/question/16688824

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