The diagram shows a sector of a circle radius 11cm.
show that perimeter of the sectors is greater that 47.5cm

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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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

we have

substitute

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

step 3

Find the perimeter of the sectors

The perimeter is equal to

substitute

assume

therefore

The perimeter of the sectors is greater than 47.5 cm