General formula to find the area of a circle [tex]\boxed{a= \pi \times r^{2}}[/tex] To find a sector area of a circle [tex]\boxed{\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}}[/tex]
NUMBER 14 Given information: r = 12 cm degree of sector = 110° (use the angle on the shaded area)
The area of the sector: [tex]\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}[/tex] [tex]\text{sector}= \dfrac{110^{0}}{360^{0}} \times \pi \times 12^{2}[/tex] [tex]\text{sector}= \dfrac{11}{36} \times \pi \times 144[/tex] [tex]\text{sector}= \dfrac{1584}{36} \pi [/tex] [tex]\text{sector}= 44 \pi [/tex] sector = 44 × 3.14 sector = 138.16
The area is 44π ≈ 138.16 cm²
NUMBER 16 Given information: r = 30 yards degree of sector = 15° (use the angle on the shaded area)
The area of the sector: [tex]\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}[/tex] [tex]\text{sector}= \dfrac{15^{0}}{360^{0}} \times \pi \times 30^{2}[/tex] [tex]\text{sector}= \dfrac{1}{24} \times \pi \times 900[/tex] [tex]\text{sector}= \dfrac{900}{24} \pi [/tex] [tex]\text{sector}= 37.5 \pi [/tex] sector = 37.5 × 3.14 sector = 117.75
