Question

The diagram shows a sector of a circle with radius 15 cm.

Calculate the perimeter of this sector.​

Answer 1

36.81 cm to the nearest hundredth (or 30 + 13 π / 6).

Explanation:

The perimeter of the circle of which this sector is a part = 2 π 15

= 30 π cms

So the length of the curved part of the sector = 26 * 30 π / 360

= 2.167π

The perimeter = 2(15) + 2.167 π

= 36.81 cm.

Answer 2

≈ 36.81 cm ( to 2 dec. places )

Explanation:

The perimeter (P) of the sector is calculated as

P = circumference of circle × fraction of circle + radii

= 2π × 15 ×
`(26)/(360)` + 30

= 30π ×
`(26)/(360)` + 30

=
`(26\pi )/(12)` + 30 ≈ 36.81 cm