2 Answers

Jochen Ritzel · Answer 1 · 2021-06-05T01:18:42+0000

The circumference and length of the darkened part of the arc are:

Circumference = 18π

Arc length = 18π/5.

In Mathematics and Eulidean Geometry, the circumference of a circle can be calculated by using the following mathematical equation (formula):

C = 2πr

Where:

By substituting the radius, we have:

C = 2π × 9

C = 18π units.

In Mathematics and Geometry, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

Where:

Since the circle is divided into five equal parts, the central angle is given by;

θ = 360/5

θ = 72°

Arc length = rθ

Arc length = 9 × 72 × π/180

Arc length = 9 × 2 × π/5

Arc length = 18π/5

VansFannel · Answer 2 · 2021-06-06T17:56:05+0000

Circumference = 56.52

Length of the darkened part of the arc = 3.6π

Solution:

Radius of the circle = 9

Circumference of the circle = 2πr

= 2 × π × 9

Circumference of the circle = 18π

Equal number of parts = 5

Total degree of circle = 360°

Degree of the darkened part =
$(360^\circ)/(5)= 72^\circ$

$$\text {Arc length}=18 \pi \left((\theta)/(360^\circ)\right)$

$$=18 \pi\left((72^\circ)/(360^\circ)\right)$

= 3.6π

Circumference = 18π

Length of the darkened part of the arc = 3.6π

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