Question

choose the correct one!

Answer 1

the answer is 154cm²

Answer 2

Answer:  The correct option is (D) 154 cm².

Step-by-step explanation:  Given that a steel wire when bent in the form of a square encloses an area of 121 sq. cm.

We are to find the area of the circle, if the same wire is bent into the form of a circle.

Let l represents the length of a side of the square and r represents the length of the radius of the circle.

Then, the perimeter of both the square and circle should be same and is equal to the length of the wire.

According to the given information, we have

$l^2=121\\\\\Rightarrow l^2=11^2\\\\\Rightarrow l=11.$

So, the perimeter of the square is given by

$P_s=l+l+l+l=11+11+11+11=44~\textup{cm}.$

Then, we must have

$\textup{perimeter of the circle}=44~\textup{cm}\\\\\Rightarrow 2\pi r=44\\\\\\\Rightarrow 2\times\dfrac{22}{7}\times r=44\\\\\Rightarrow r=7~\textup{cm}.$

Therefore, the AREA of the circle is given by

$A_c=\pi r^2=\dfrac{22}{7}\times7^2=22\times7=154~\textup{cm}^2.$

Thus, the required area of the circle is 154 cm².

Option (D) is correct.