Question

Which shows the length of the darkened arc? (The wierd symbol next to the answers is Pi)​

Answer 1

Answer: 15 π

Step-by-step explanation:

The formula for determining the circumference of a circle is expressed as

Circumference = 2πr

Looking at the circle,

Diameter = 18 inches

Radius = diameter/2 = 18/2

Radius = 9 inches

Circumference = 2 × 9 × π = 18π

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r = 9 inches

θ = 60 degrees

Length of arc = 60/360 × 2 × π × 9

Length of arc = 3π

The length of the darkened arc is the circumference of the circle - the arc formed by 60 degrees. Therefore,

length of the darkened arc = 18π - 3π = 15π

Answer 2

Answer:

15 pi

Step-by-step explanation:

The circumference of the circle is given by

C = pi * d

C = pi *18

We are subtracting part of the circumference that covers 60 degrees

The entire circle is 360 degrees

60/360 = 1/6

We are subtracting 1/6 of the circumference

1/6 *18pi = 3pi

We have 18pi and subtract 3pi = 15pi

The dark shaded arc is 15pi