Question

a piece of wire is in the form of a rectangle whose length and breadth are 35 cm and 31 CM respectively it is very bent in the form of a circle find the radius of the circle​

Answer 1

Given

• A piece of wire is in the form of a rectangle whose dimensions are :-
• Length of the rectangle = 35 cm
• Breadth of the rectangle = 31 cm
• The same wire is bent in the form of circle.

To find

• Radius of the circle

Concept

We are given that a piece of wire which is in the form of rectangle is bent in the form of circle and we have to find the radius. So, we will find the value of the boundary of the rectangle, i.e. perimeter. The perimeter of the rectangle will be equal to the circumference of the circle.

Reason :- The same wire is bent in the form of circle. So, its dimensions are same and hence, the perimeter will also be same.

Solution

Using formula,

❖ Perimeter of rectangle = 2(l + b)

where,

• l = length of the rectangle
• b = breadth of the rectangle

Substituting the given values,

⟼ Perimeter = 2(35 + 31)

⟼ Perimeter = 2(66)

⟼ Perimeter = 132 cm

★ Perimeter of the rectangle = 132 cm

⋄ Perimeter of the rectangle = Circumference of the circle

• Formula to be used :-

❖ Circumference of the circle = 2πr

where,

• Take π = 22/7
• r = radius of the circle

⟼ 132 = 2 × 22/7 × r

⟼ 132 = 44/7 × r

⟼ 132 × 7/44 = r

⟼ 21 = r

★ Radius of the circle = 21 cm