Discussion
A wire is in the shape of a rectangle whose area is 7260 \(\text{cm}^2\) and sides are in the ratio 5 : 3. The same wire is bent to form a circle. What is the area (in \(\text{cm}^2\)) of the circle? (Use \(\pi = \frac{22}{7}\))
Answer: C
The area of the circle is 9856 cm². Let the sides of the rectangle be 5k and 3k. Then 15k² = 7260, so k² = 484 and k = 22, and the sides are 110 cm and 66 cm. The wire has length equal to the perimeter:
\[ 2(110 + 66) = 352 \text{ cm} \]
Bent into a circle, 2πr = 352, so with π = 22/7, r = 56 cm.
\[ \text{Area} = \frac{22}{7} \times 56^2 \]
\[ = 22 \times 448 = 9856 \text{ cm}^2 \]
The options 7304, 7546 and 12474 are not the area of a circle of radius 56 cm, so the third option is correct.
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