Question

A copper wire when bent in the form of a square encloses an area of 484 sq. cm if the same wire is bent in the form of a circle then the area enclosed by it is $(\pi = \dfrac{{22}}{7})$
A) $412c{m^2}$
B) $616c{m^2}$
C) $500c{m^2}$
D) None of these

Answer 1

Hint: Circumference of circle is equal to the length of the wire so here in this question we will first evaluate the length of the wire by using formula of area of square as $sid{e^2}$ and by using perimeter of square as $4 \times side.$

Complete step-by-step answer:
Given that Area of the square formed by bending a copper wire $ = 484c{m^2}$
We know that area of the square $ = {s^2}$
$
   \Rightarrow {s^2} = 484 \\
   \Rightarrow s = 22cm \\
 $
We know that perimeter of the square
$
   = 4 \times s \\
   = 4 \times 22 \\
   = 88cm \\
 $
Therefore the length of the wire $ = 88cm$
Now,
Given that the same wire is bent into a form of circle.
Circumference of circle = Length of wire
$
   \Rightarrow 2 \times \pi \times r = 88 \\
   \Rightarrow 2 \times \dfrac{{22}}{7} \times r = 88 \\
   \Rightarrow 44 \times r = 88 \times 7 \\
   \Rightarrow 44 \times r = 616 \\
   \Rightarrow r = \dfrac{{616}}{{44}} \\
   \Rightarrow r = 14cm \\
$
We know that area of circle
$
   = \pi {r^2} \\
   = \dfrac{{22}}{7} \times {14^2} \\
   = 616c{m^2} \\
 $
Therefore the area enclosed by the circle is $616c{m^2}$.

Note: In order to solve these types of problems related to finding the area or volume and some parameters are missing such as radius for circle and side for square are not given directly in the question. Then search for the conditions given in the question to find the missing parameters. Sometimes areas are given such as in this problem. Sometimes they may give circumference.