A wire is bent in the form of a square encloses an area of 121 sq.Cm. If the wire is bent in the form of a circle, then what would br the area?
Answers
484
π
c
m
2
≈
154.061984913
c
m
2
Explanation:
First we need to find the length of the wire.
To do that, we should try to figure out the length of 1 side of the square
Area of a square
=
(
s
i
d
e
)
2
that means that a
(
s
i
d
e
)
=
√
121
if the Area of the square was 121.
therefore one side of the square would be
√
121
=
11
The Perimeter of the square would be equal to the full length of the copper wire.
Perimeter of a square
=
4
(
s
i
d
e
)
since we just found that
(
s
i
d
e
)
=
11
we can determine that the Perimeter would be
11
⋅
4
=
44
Therefore the length of the copper wire would be
44
c
m
long
-
If we make a circle from this wire, the length of the wire would then be the Circumference of the Circle.
Circumference of a Circle
=
2
π
(
r
a
d
i
u
s
)
from this we can get that
(
r
a
d
i
u
s
)
=
44
2
π
=
22
π
Then, the Area of the Circle would be
Area of a Circle
=
π
(
r
a
d
i
u
s
)
2
Since we found that
(
r
a
d
i
u
s
)
=
22
π
we can figure out that the Area of the Circle would be
π
(
22
π
)
2
=
484
π
≈
154.061984913
←
answer