question_answer

A copper wire, when bent in the form of a square encloses an area of 121\[c{{m}^{2}}\]. If the same wire is bent in the form of a circle, find the area enclosed by it.

Answer:

Area enclosed the copper wire

In square shape \[={{\left( side \right)}^{2}}\]

∴                      \[{{\left( side \right)}^{2}}=121\text{ }c{{m}^{2}}\]

side\[=\sqrt{121}=11\text{ }cm\].

Hence length of wire = 11 × 4

= 44 cm

New length = Circumference of the circle

2πr = 44

\[2\times \frac{22}{7}\times r=44\]

\[r=\frac{44}{2\times 22}\times 7\]

Thus,    r = 7 cm

Hence, area enclosed by the wire when it is bent in circular shape

\[=\pi {{r}^{2}}\]

\[=\frac{22}{7}\times {{\left( 7 \right)}^{2}}\]

\[=\frac{22}{7}\times 7\times 7\]

\[=\text{ }154\text{ }{{m}^{2}}.\]