A sector of a circle of radius 21\text{ cm} has a total perimeter of 64\text{ cm}. Calcula… — JAMB UTME

A sector of a circle of radius $21\text{ cm}$ has a total perimeter of $64\text{ cm}$ . Calculate the area of the sector in $\text{cm}^2$ . (Take $\pi = \frac{22}{7}$ )

Answer: 231 cm^2

Answer

The area of the sector is

231\text{ cm}^2

The total perimeter of a sector is given by

P = 2r + l

. Given radius

r = 21\text{ cm}

and perimeter

P = 64\text{ cm}

, the arc length is

l = 64 - 2(21) = 22\text{ cm}

. The area of the sector is calculated using

A = \frac{1}{2} r l = \frac{1}{2} \times 21 \times 22 = 231\text{ cm}^2

Step-by-Step Solution

Find the arc length of the sector

The arc length

l = 22\text{ cm}

The total perimeter of a sector includes its arc length plus its two bounding radii (

P = 2r + l

). Subtracting

2r = 42\text{ cm}

from

64\text{ cm}

gives

l = 22\text{ cm}

Calculate the area of the sector

The area

A = 231\text{ cm}^2

Using the relation between arc length and sector area,

A = \frac{1}{2} r l = \frac{1}{2} \times 21 \times 22 = 231\text{ cm}^2

Key Concept

Perimeter and Area of a Sector of a Circle

Estimated Time:1m 30s

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