Discussion
A circular wire of radius 21cm is cut and bent to form in the form of a rectangle whose sides are in the ratio of 6:5. Assuming, Π = 22/7, the area enclosed by the rectangle is
Answer: B
Bending conserves the length of the wire, so the circle's circumference becomes the rectangle's perimeter.
\[ C = 2\pi r = 2 \times \frac{22}{7} \times 21 = 132 \text{ cm} \]
With sides \( 6x \) and \( 5x \):
\[ 2(6x + 5x) = 132 \quad\Longrightarrow\quad 22x = 132 \quad\Longrightarrow\quad x = 6 \]
\[ \text{sides} = 36 \text{ cm and } 30 \text{ cm} \]
\[ \text{area} = 36 \times 30 = 1080 \text{ cm}^{2} \]
It is the perimeter that is preserved, not the area: the circle enclosed \( \pi r^{2} = 1386 \) cm², noticeably more than the rectangle. A circle always encloses the most area for a given perimeter.
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