Question

(i) The perimeter of a sector of a circle is 58 cm. Find the area if its diameter is 9 cm.
(ii) Find the area of a sector whose radius and perimeter are 20 cm and 110 cm respectively.

Answer 1

i)$D=4㎝\Rightarrow r=\frac{9}{2}=4.5㎝$

$\frac{\theta }{360°}\times 2\pi r+2r=58㎝\Rightarrow \frac{\theta }{360°}\times 2\times \frac{22}{7}\times 4.5+2\times 4.5=58$

$\frac{198\theta }{360°\times 7}+9=58\Rightarrow \theta =\frac{7\times 360°}{198}(58-9)=623.64°$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{623.64°}{360°}\times \frac{22}{7}\times 4.5\times 4.5=110.25㎠$

ii)$\frac{\theta }{360°}\times 2\pi r+2r=110㎝$

$\Rightarrow \frac{\theta }{360°}\times 2\times \frac{22}{7}\times 20+(2\times 20)=110㎝$

$\Rightarrow \frac{880\theta }{360°\times 7}=70㎝\Rightarrow \theta =\frac{70\times 360°\times 7}{880}=200.45°$

Area$=\frac{\theta }{360°}\times \pi r^2=\frac{200.45°}{360°}\times \frac{22}{7}\times 20\times 20=699.98㎠$