The radius of a sector of a circle is 30 cm. The arc subtends an angle of 72 degrees at the centre of the circle.

1. Calculate the perimeter of the sector
2. Work out the area of the sector

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We are given:

Radius r = 30 cm

Angle at the centre θ = 72°

Full angle in a circle = 360°

We’ll calculate:

1. Perimeter of the sector
2. Area of the sector

1. Perimeter of a Sector

The perimeter consists of:

Two radii (2 r) + the arc length

Arc Length Formula:

Arc length = ^θ/_360°  × 2 π r

= ⁷²/₃₆₀ × 2 π × 30

= ¹/₅ × 60 π

=12 π

= 12(3.14)

Arc length = 37.70

Total Perimeter:

Perimeter= 2 r + Arc length

= 2 × 30 + 37.70 = 97.70 cm

Perimeter = 97.70 cm

2. Area of a Sector

Area Formula:

Area = ^θ/_360°  × π r ²

= ⁷²/₃₆₀ × π × 30²

=¹/₅ × π × 900

=180 π 

= 180 (3.14)

= 565.2 cm ²

Final Answers:

Perimeter = 97.70 cm

Area = 565.2 cm ²

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