Question

a copper wire of length of 44cm is to be bent into a square and a circle.Which will have a larger area

Answer 1

Step-by-step explanation:

∴ The circumference of the circle=2πr=44cm

⇒2×

7/22

×r=44⇒r=

2×22

44×7=7cm

Now, Area of the circle=πr

2= 7

22×7×7=154cm

2

Now the wire is converted into square,

Then perimeter of square=44cm

⇒4× side=44

⇒ side= 4

44=11cm

Now, area of square=side×side=11×11=121cm 2

Answer 2

Given : Length of copper wire = 44 cm

To find : If the wire is bent into a square and a circle, then which shape will have the larger area?

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

In the case of a square :

• Perimeter of the square = Length of the wire = 44 cm
• Length of a side of the square = 44/4 = 11 cm
• Area of the square = (side)² = (11)² = 121 cm²

In the case of a circle :

• Circumference of the circle = 44 cm
• Radius of the circle = Circumference ÷ (2π) = 44 ÷ (2 × 22/7) = 44 × (1/2) × (7/22) = 7 cm
• Area of the circle = π × (radius)² = 22/7 × (7)² = 154 cm²

Now, it is clear that the area of the circle is greater than the area of the square. (154 > 121)

Hence, the circle will have the larger area.