Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?

Solution:

It is given that

Radius of the circle = 14 cm

Length of the rectangle = 24 cm

We know that

Length of the wire = Circumference of the circle

= 2πr

Substituting the values

= 2 × 22/7 × 14

= 88 cm

Consider b as the width of rectangle

As the wire is rebent in the form of a rectangle

Perimeter of rectangle = Circumference of the circle

2 (24 + b) = 88

Dividing both sides by 2

24 + b = 44

b = 44 - 24

b = 20 cm

Here

Area of circle = πr²

Substituting the values

= 22/7 × 14²

= 616 cm²

Area of rectangle = l × b

Substituting the values

= 24 × 20

= 480 cm²

Therefore, the circle encloses more area than the rectangle.

✦ Try This: Sudha took a wire and bent it to form a circle of radius 24 cm. Then she bent it into a rectangle with one side 34 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 108

Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?

Summary:

Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. The length of the wire is 88 cm. The circle encloses more area than the rectangle.

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