A steel wire, when bent in the form of a square, encloses an area of 1

1.	A steel wire, when bent in the form of a square, encloses an area of 121 cm2. The same wire is bent in the form of a circle. Find the area of the circle.
Answer» Let the side length of square is a cm. Given that the area of square is 121 cm². Therefore, a² = 121 ⇒ a = 11 cm. Since, the same wire is bent in the form of circle. ∴ The circumference of the circle is equal to the perimeter of the square. Hence, 2\(\pi r\) = 4a = 4× 11 = 44 cm. ⇒ r = \(\frac{44}{2\pi}=\frac{44}{2\times{\frac{22}{7}}}\) = 7cm. Hence, the radius of the circle is r = 7cm. Now, the area of the circle = \(\pi r\)² = \(\frac{22}{7}\times7^2\) = 22 × 7 = 154 cm². Hence, the area of the circle is 154 cm².

A steel wire, when bent in the form of a square, encloses an area of 121 cm2. The same wire is bent in the form of a circle. Find the area of the circle.

Answer»

Let the side length of square is a cm.

Given that the area of square is 121 cm².

Therefore, a² = 121

⇒ a = 11 cm.

Since, the same wire is bent in the form of circle.

∴ The circumference of the circle is equal to the perimeter of the square.

Hence, 2\(\pi r\) = 4a = 4× 11 = 44 cm.

⇒ r = \(\frac{44}{2\pi}=\frac{44}{2\times{\frac{22}{7}}}\) = 7cm.

Hence, the radius of the circle is r = 7cm.

Now, the area of the circle = \(\pi r\)² = \(\frac{22}{7}\times7^2\) = 22 × 7 = 154 cm².

Hence, the area of the circle is 154 cm².

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