Question

A piece of wire is in the form of a rectangle 15cm long and 7cm broad is reshaped and bent into the form of a circle. Find the radius of the circle.
(a)5cm
(b)7cm
(c)8cm
(d)9cm

Answer 1

Hint: A piece of wire is reshaped to a circle. So the perimeter of the rectangle formed by wire will be equal to the circumference of the circle formed. Solve the radius of the circle.

Complete step-by-step answer:
It is said that a piece of wire is in the form of a rectangle.
The length of the rectangle = 15cm.
Breadth of a rectangle = 7cm.
Now it is said that the wire is reshaped in the form of a circle. As it is reshaped the length of wire will remain the same. Let’s consider the radius of the circle as ‘r’.
Thus the perimeter of rectangle = 2 (length + breadth)
                                                          = \[2\left( 15+7 \right)=2\times 22=44\]
We know the perimeter of circle = \[2\pi r\].
\[\therefore \]Perimeter of rectangle = Perimeter of circle.
\[\Rightarrow 2\pi r=44\][Take, \[\pi =\dfrac{22}{7}\]]
\[\begin{align}
  & 2\times \dfrac{22}{7}\times r=44 \\
 & \therefore r=\dfrac{44\times 7}{2\times 22}=7 \\
\end{align}\]
Thus, we got the radius of the circle, r = 7cm.
\[\therefore \] Option (b) is the correct answer.

Note: We are told that the wire is reshaped and its not completely moulded. So their perimeter will be the same. Don’t mistakenly assume that their volume will be the same as the height of the rectangle formed by the triangle are not given.