Question

Find the arc length, area and perimeter of the sector with
(i) radius 21 cm and central angle ${60}^o$
(ii) radius 4.9 cm and central angle ${30}^o$
(iii) radius 14 cm and sector angle ${45}^o$
(iv) radius 15 cm and sector angle ${63}^o$
(v) radius 21 dm and sector angle ${240}^o$

Answer 1

i)Arc length$=\frac{\theta }{360°}\times 2\pi r=\frac{60°}{360°}\times 2\times \frac{22}{7}\times 21=22㎝$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{60°}{360°}\times \frac{22}{7}\times 21\times 21=231㎠$

Perimeter=Arc length$+2r=22+(2\times 21)=64㎝$

ii)Arc length$=\frac{\theta }{360°}\times 2\pi r=\frac{30°}{360°}\times 2\times \frac{22}{7}\times 4.9=\frac{7.7}{3}㎝$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{30°}{360°}\times \frac{22}{7}\times 4.9\times 4.9=\frac{37.73}{6}㎝$

Perimeter=Arc length$+2r=\frac{7.7}{3}+(2\times 4.9)=\frac{7.7}{3}+9.8=\frac{37.1}{3}㎝$

iii)Arc length$=\frac{\theta }{360°}\times 2\pi r=\frac{45°}{360°}\times 2\times \frac{22}{7}\times 14=11㎝$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{1}{8}\times \frac{22}{7}\times 14\times 14=77㎠$

Perimeter=Arc length$+2r=11+(2\times 14)=39㎝$

iv)Arc length$=\frac{\theta }{360°}\times 2\pi r=\frac{63°}{360°}\times 2\times \frac{22}{7}\times 15=16.5㎝$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{63°}{360°}\times \frac{22}{7}\times 15\times 15=123.75㎠$

Perimeter=Arc length$+2r=16.5+(2\times 15)=46.5㎝$

v)Arc length$=\frac{\theta }{360°}\times 2\pi r=\frac{240°}{360°}\times 2\times \frac{22}{7}\times 21=88dm$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{240°}{360°}\times \frac{22}{7}\times 21\times 21=924d㎡$

Perimeter=Arc length$+2r=88+(2\times 21)=130dm$