Question

5. A wire of length 176 cm is first bent into a square and then into a circle. Which one will have more area?

Answer 1

GIVEN THAT

A wire of length 176 cm is bent into a square.

And then, the wire bent into a circle.

TO FIND

Which one will have more area ?

FORMULA USED

Perimeter of square = 4 × side

Area of square = side × side

Circumference of circle = 2 × π × r

Area of circle = π × r²

SOLUTION

Perimeter of square = 4 × side

= 4 × side = 176

= side = 176

4

= side = 44 cm

So, side of square is 44 cm

Area of square = side × side

= ( 44 × 44 ) cm²

= 1936 cm²

So, area of square is 1936 cm²

NOW,

Then, the wire is bent into a circle.

Circumference of circle = 2 × π × r

= 2 × 22 × r = 176

7

= 44 × r = 176 × 7

= r = 176 × 7

44

= r = 4 × 7

= r = 28

So, radius of circle is 28 cm

Area of circle = π × r²

= 22 × 28 × 28

7

= 22 × 4 × 28

= 2464

So, area of circle is 2464 cm²

AND,

2464 > 1936

So, circle have more area by

= (2464 - 1936)cm²

= 528 cm²

So, circle have more area by 528 cm²