Question : The perimeter of a sheet of paper in the shape of a quadrant of the circle is 75 cm. Its area would be $(\pi=\frac{22}{7})$
Option 1: 100 cm2
Option 2: 346.5 cm2
Option 3: 693 cm2
Option 4: 512.25 cm2
Correct Answer: 346.5 cm 2
Solution : Let the radius of the circle be $r$ cm. Perimeter of quadrant = $2r+\frac{1}{4}\times 2\pi r$ So, $2r+\frac{1}{2}\pi r=75$ ⇒ $r(2+\frac{11}{7})=75$ ⇒ $r=\frac{75\times 7}{25}$ ⇒ $r=21$ cm Area of quadrant = $\frac{1}{4}\pi r^2$ = $\frac{1}{4}\times \frac{22}{7}\times 21^2$ = 346.5 cm 2 Hence, the correct answer is 346.5 cm 2 .
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