Question : An arc of length 23.1 cm subtends an 18° angle at the centre. What is the area of the circle?
$\mathrm{[Use ~\pi=\frac{22}{7} ]}$
Option 1: 16978.50 cm2
Option 2: 16988.50 cm2
Option 3: 16878.50 cm2
Option 4: 16798.50 cm2
Correct Answer: 16978.50 cm 2
Solution :
Arc length = 23.1 cm
⇒ $\frac{\theta}{360^{\circ}}× 2\pi r$ = 23.1
⇒ $\frac{18^{\circ}}{360^{\circ}}× 2\pi r$ = 23.1
⇒ $r=73.5$ cm
Area of circle = $\pi$r$^{2}$ = ${\frac{22}{7}}\times{73.5}\times{73.5}$ = 16978.50 cm$^{2}$.
Hence, the correct answer is 16978.50 cm
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