A copper wire of length 44 cm is to be bent into a square and a circle. Which will have a larger area?
Answers
Step-by-step explanation:
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
Step-by-step explanation:
Given :-
A copper wire of length 44 cm is to be bent into a square and a circle.
To find:
Which will have a larger area?
Solution:-
The length of the copper wire=44cm
1)If it is bent into a square then the length of the wire becomes it's perimeter
Perimeter of the square=4×side
=>4×side=44
=>Side=44/4
=>side=11cm
The length of the side of the square=11 cm
Area of the square=side×side sq.units
=>Area=11×11
=>Area of the square=121 sq.cm--------(1)
2)If it is bent into a circle then the length of the wire becomes the circumference of the circle
=>Circumference of the circle=2πr units
=>2πr=44
=>2×(22/7)×r=44
=>44r/7=44
=>r=44×7/44
=>r=7cm
The radius of the circle=7cm
Now area of the circle=πr² sq. units
=>π(7)²
=>(22/7)(7²)
=>22×7
Area of the circle =154sq.cm-------(2)
From (1)&(2)
Area of the square =121sq.cm
Area of the circle=154 sq.cm
Answer:-
Area of the circle is greater than the area of the square