A piece of wire of length 88\text{ cm} is bent to form the perimeter of a sector of a circ… — JAMB UTME

A piece of wire of length $88\text{ cm}$ is bent to form the perimeter of a sector of a circle of radius $21\text{ cm}$ . What is the area of the sector in $\text{cm}^2$ ?

Answer: 483 cm²

Answer

The area of the sector is

483\text{ cm}^2

The total length of the wire forms the perimeter of the sector, which consists of two radii and the arc length (

P = 2r + l

). With

P = 88\text{ cm}

and

r = 21\text{ cm}

, the arc length is

l = 88 - 2(21) = 46\text{ cm}

. Using the sector area formula

A = \frac{1}{2} r l

, the area is

\frac{1}{2} \times 21 \times 46 = 483\text{ cm}^2

Step-by-Step Solution

Determine the arc length of the sector from the given perimeter

l = 46\text{ cm}

The total perimeter of a sector includes two straight radii and the curved arc length:

P = 2r + l

. Subtracting twice the radius (

2 \times 21 = 42\text{ cm}

) from the total wire length of

88\text{ cm}

gives an arc length of

46\text{ cm}

Calculate the area of the sector

A = 483\text{ cm}^2

The area of a sector can be computed using the formula

A = \frac{1}{2} r l

. Substituting

r = 21\text{ cm}

and

l = 46\text{ cm}

yields

A = \frac{1}{2} \times 21 \times 46 = 483\text{ cm}^2

Key Concept

Perimeter and Area of a Sector of a Circle

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