Question : A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is: (take $\pi=\frac{22}{7}$)
Option 1: 125 cm2
Option 2: 230 cm2
Option 3: 550 cm2
Option 4: 616 cm2
Correct Answer: 616 cm 2
Solution :
Given:
A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm.
So the perimeter of the rectangle is = 2 × (18 + 26) = 88 cm
According to the question,
The circumference of the circle is 88 cm.
So, $2\pi r=88$
⇒ $\frac{2×22×r}{7}=88$
⇒ $r=\frac{88×7}{2×22}$
⇒ $r=14$
So, the area of the circle is = $\pi r^2$ = $\frac{22}{7}×14×14$ = $616$ cm
2
.
Hence, the correct answer is 616 cm
2
.
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