A sector of a circle of radius 21\text{ cm} subtends an angle of 60^\circ at the centre of… — JAMB UTME

A sector of a circle of radius $21\text{ cm}$ subtends an angle of $60^\circ$ at the centre of the circle. What is the total perimeter of the sector? (Take $\pi = \frac{22}{7}$ )

A
$22\text{ cm}$
B
$43\text{ cm}$
$64\text{ cm}$ Answer
D
$231\text{ cm}$

Answer

The total perimeter of the sector is

64\text{ cm}

The perimeter of a sector consists of its curved arc length plus its two bounding radii (

2r

). Using

\theta = 60^\circ

r = 21\text{ cm}

, and

\pi = \frac{22}{7}

, the arc length is

\frac{60}{360} \times 2 \times \frac{22}{7} \times 21 = 22\text{ cm}

. Adding

2 \times 21\text{ cm} = 42\text{ cm}

yields

64\text{ cm}

Step-by-Step Solution

Calculate the arc length (

s

) of the sector using the formula

s = \frac{\theta}{360^\circ} \times 2\pi r

s = \frac{60^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 21 = \frac{1}{6} \times 132 = 22\text{ cm}

The arc length represents the curved boundary of the sector.

Calculate the total perimeter of the sector by adding the arc length and the two bounding radii:

P = s + 2r

P = 22\text{ cm} + 2(21\text{ cm}) = 22 + 42 = 64\text{ cm}

A sector boundary consists of the curved arc plus the two straight radial edges.

Key Concept

Perimeter of a circular sector

Estimated Time:1m 30s

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