Examkin

Soru

Zorluk: OrtaPerimeter and Area of Plane Shapes

A sector of a circle of radius 21 cm21\text{ cm} has a total perimeter of 64 cm64\text{ cm}. Calculate the area of the sector in cm2\text{cm}^2. (Take π=227\pi = \frac{22}{7})

Cevap: 231 cm^2

Cevap

The area of the sector is 231 cm2231\text{ cm}^2.
The total perimeter of a sector is given by P=2r+lP = 2r + l. Given radius r=21 cmr = 21\text{ cm} and perimeter P=64 cmP = 64\text{ cm}, the arc length is l=64−2(21)=22 cml = 64 - 2(21) = 22\text{ cm}. The area of the sector is calculated using A=12rl=12×21×22=231 cm2A = \frac{1}{2} r l = \frac{1}{2} \times 21 \times 22 = 231\text{ cm}^2.

Adım Adım Çözüm

1
Find the arc length of the sector
The arc length l=22 cml = 22\text{ cm}
The total perimeter of a sector includes its arc length plus its two bounding radii (P=2r+lP = 2r + l). Subtracting 2r=42 cm2r = 42\text{ cm} from 64 cm64\text{ cm} gives l=22 cml = 22\text{ cm}.
2
Calculate the area of the sector
The area A=231 cm2A = 231\text{ cm}^2
Using the relation between arc length and sector area, A=12rl=12×21×22=231 cm2A = \frac{1}{2} r l = \frac{1}{2} \times 21 \times 22 = 231\text{ cm}^2.

Anahtar Kavram

Perimeter and Area of a Sector of a Circle
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Perimeter and Area of Plane Shapes

Bu konudan daha fazla soru