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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