A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in
the shape of a square and then into a circle, find: (i) the side of the square
(ii) the radius of the circle.
Answers
Total Length is wire is 40+ 22 = 62 centimetre
Side of square is 62/4 is 15.5 cm
Perimeter of circle 2pie radius
Radius of circle= 9.86 cm
Answer:
⇒ Side of the Square = 31cm
⇒ Radius of the circle = 19.72cm
Step-by-step explanation:
Given:
⇒ A wire is shaped in the form of rectangle.
⇒ Length of the wire = 40cm
⇒ Breadth of the wire = 22cm
We need to find:
If the rectangular wire is rebent in the shape of a square and then into a circle, we need to find:
⇒ The side of the square.
⇒ The radius of the circle.
Solution:
First, let's find the perimeter of the rectangular wire.
⇒ Perimeter of the wire = 2(Length+Breadth)
⇒ Perimeter of the wire = 2(40+22)
⇒ Perimeter of the wire = 2(62)
⇒ Perimeter of the wire = 124cm
The wire is rebent in the shape of a square and circle. This implies that though there is a change in the shape of the wire, their perimeters are unchanged and are equal. This means:
⇒ Perimeter of Rectangle = Perimeter of Square
⇒ Perimeter of Square = 124
⇒ 4×Side = 124
⇒ Side = 124/4
⇒ Side = 31cm
(i) Hence, the side of the square is 31cm
We know that Perimeter of a circle is nothing but the circumference. Let's find the radius of the circle:
⇒ Circumference = 2πr
As we know that the perimeter of the rectangle is also equal to circumference of the circle,
⇒ Circumference of the circle = 124cm
⇒ 2πr = 124
⇒ 2×22/7×r = 124
⇒ 44r/7 = 124
⇒ 44r = 124×7
⇒ 44r = 868
⇒ r = 868/44
⇒ r = 19.72cm
(ii) Hence, the radius of the circle is 19.72cm