Respuesta :

calculista

Answer:

The perimeter of the sectors is greater than 47.5 cm

Step-by-step explanation:

step 1

Find the circumference of the complete circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=11\ cm[/tex]

substitute

[tex]C=2\pi (11)[/tex]

[tex]C=22\pi\ cm[/tex]

step 2

Find the length of the arc of the sector

we know that

The circumference subtends a central angle of 360 degrees

so

using proportion

Find out the length of the arc by a central angle of 135 degrees

[tex]\frac{22\pi }{360^o}=\frac{x}{135^o} \\\\x=22\pi (135)/360\\\\x=8.25\pi \ cm[/tex]

step 3

Find the perimeter of the sectors

The perimeter is equal to

[tex]P=2r+8.25\pi[/tex]

substitute

[tex]P=2(11)+8.25\pi[/tex]

[tex]P=(22+8.25\pi)\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]P=(22+8.25(3.14))=47.9\ cm[/tex]

therefore

The perimeter of the sectors is greater than 47.5 cm

raphealnwobi

Hence the perimeter of the sector is 25.9 cm.

The perimeter of a sector with a central angle (θ) is given by:

Perimeter = (θ/360) × 2πr

Where r is the radius of the circle and θ is the central angle.

From the diagram attached, θ is 135°. Hence, the area of the sector is:

Perimeter = (θ/360) × 2πr

Perimeter = (135/360) × 2π(11)

Perimeter of sector = 25.9 cm

Hence the perimeter of the sector is 25.9 cm.

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