A copper wire, when bent in the form of a square encloses an area of 484 cm². If the same wire is bent in the form of a circle. Find the area of the circle enclosed by given wire.
Answers
Given,
A copper wire when bent in the form of a square encloses an area of 225cm².
To find,
The area of the circle, if the same wire is bent into the form of a circle.
Solution,
We can simply solve this mathematical problem by using the following mathematical process.
The area of the square = 225 cm²
Let, the length of the side of the square =
a cm
Area = (axa) = a² cm²
According to the data mentioned in the question,
a² = 225
a = √225
a = 15 cm
So, the length of the side of the square = 15 cm
The perimeter of the square = (4×15) = 60cm
Here, the wire itself is bent into the shape of a square. So. the perimeter of the square will be the length of the wire.
Length of the wire = 60 cm
If the wire is bent into the shape of a circle, then the length of the wire will become the perimeter of the circle.
So, perimeter of the circle = 60 cm
Let, the radius = r cm
Perimeter = 2₁ cm
According to the data mentioned in the question,
2πr: = 60
r = 60/2T
r = 30/π cm
So,
The area of the circle = π × (30/1)² = 900/ π = 900 ÷ (22/7) = 900 × (7/22) = 286.36 cm²
Hence, the area of the circle will be 286.36 cm².
Answer:
616cm square
Step-by-step explanation:
area of the square=484cm square
let the side be X
area of the square=X × X
484 cm square=X square
484cm square=√484=22
perimeter of square=4×22=88
perimeter of square=2πr
88=2πr
r =88/2π =44/22×7 =44×7/22=14 cm
area of circular field =πr square
area of circular field=22/7×14×14 ( 14 divided by 7 and the quotient is 2)
=22×2×14=616 (calculate,you will get 616)
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