Question

A brass wire with circular shape with radius $\dfrac{2}{\pi }$ is bent into a square. Determine the side of the square.
(a) 2
(b) 1
(c) $\dfrac{1}{2}$
(d)None of these

Answer 1

Hint: To solve this question first we will find the perimeter of circle of radius $\dfrac{2}{\pi }$ and then perimeter of square by letting it’s side equals to x, then we will evaluate the value of x by putting perimeter of circle and square equal.

Complete step-by-step answer:
Before we solve this question, let us see what is the meaning of perimeter and what is the measure of perimeter of circle with radius and a square of side a.
Perimeter is the measure of length of outline of a 2-D surface.
Let us have a circle of radius r, then the perimeter of the circle is equal to $2\pi r$.

Let, the side of square be ‘a’ we know that square has four equal sides, then the perimeter of square is 4a.

Now, in question it is given that A brass wire with circular shape with radius$\dfrac{2}{\pi }$, so perimeter of brass wire will be $2\times \pi \times \dfrac{2}{\pi }$.
On solving, we get
Perimeter of a brass wire $=4$cm
Now, as a brass wire is turned into square, let side of square be x
So, the perimeter of the square will be 4x.
 As brass wire is changed to square from circle, the perimeter will be the same only shape is changed.
So, we can say that
4 cm = 4x cm
On solving, we get
x = 1 cm
So, the correct answer is “Option b”.

Note: To solve this question one must know the concept of perimeter and measure of various shapes such as circle, rectangle, square, triangle etc. Always remember if one shape is transformed to another shape then both shapes have the same perimeter. Try not make any calculation mistakes.