Question

Find the area and perimeter of the sector with
(i) radius 10 cm and arc length 33 cm.
(ii) radius 55 cm and arc length 80 cm.
(iii) radius 12 cm and arc length 15.25 cm.
(iv) radius 20 cm and arc length 25 cm.

Answer 1

i)$\frac{\theta }{360°}\times 2\pi r=33㎝\Rightarrow \theta =\frac{33\times 360\times 7}{44\times 10}=184°$

Area$=\frac{189°}{360°}\times \frac{22}{7}\times 10\times 10=165㎠$

Perimeter=Arc length$+2r=33+20=53㎝$

ii)$\frac{\theta }{360°}\times 2\pi r=80㎝\Rightarrow \theta =\frac{80\times 360°\times 7}{44\times 14}=83.30°$

Area$=\frac{83.30°}{360°}\times \frac{22}{7}\times 55\times 55=2199.85㎠$

Perimeter$=80+(2\times 55)=190㎝$

iii)$\frac{\theta }{360°}\times 2\pi r=15.25㎝\Rightarrow \theta =\frac{15.25\times 360\times 7}{44\times 12}=72.78°$

Area$=\frac{72.78°}{360°}\times \frac{22}{7}\times 12\times 12=91.50㎠$

Perimeter$=15.25+(2\times 12)=39.25㎝$

iv)$\frac{\theta }{360°}\times 2\pi r=25㎝\Rightarrow \theta =\frac{25\times 360°\times 7}{44\times 20}=71.60°$

Area$=\frac{71.60°}{360°}\times \frac{22}{7}\times 20\times 20=250.03㎠$

Perimeter$=25+(2\times 20)=665㎝$