Wire of length 176 cm is first bent into a square and then into a circle.
which one will have more area?
Answers
Answer:
The Area of Circle is greater than Area of Square.
Step-by-step explanation:
suppose length of wire is perimeter of square and circumference of circle
so,
perimeter = 4 x side
176 = 4 x side
176 / 4 = side
side = 44cm
Therefore Area of square = 44 x 44
= 1936 sq.cm
circumference = 2πr
176 = 2 x 3.14 x r
176 / 6.28 = r
r = 28.025
Therefore Area of Circle = π x r x r
= 3.14 x 28.025 x 28.025
= 2466.158 sq.cm
The Area of Circle is greater than Area of Square.
Answer:
Given, Total length of the wire=44cm
∴ 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
Therefore, on comparing the area of circle is greater than that of square, so the circle enclosed more area.