If the perimeter of a circle is twice the perimeter of a square, then find the ratio of their areas.
Answers
Answer:
Step-by-step explanation:
Given the perimeter of the circle is equal to that of the square.
P
circle
=P
square
Let r be the radius of the circle & a besides of square, then
2πr=4a
[
a
r
=
2π
4
=
π
2
]
Now
Areaofsquare
Areaofcircle
=
a
2
πr
2
=π(
a
r
)
2
Using
a
r
=
π
2
, we get
A
square
A
circle
=π(
π
2
)
2
=
π
2
4
×π=
π
4
Hence the ratio of Area of a circle to that of a square is
π
4
.
14:11
Let the radius of the circle =r.
∴ Its circumference =2πr and Area =πr2.
It is given that circumference of circle is same as perimeter of square.
∴ Square's one side =41× cirumference of the given circle
=41×2πr=2πr.
∴ Area of square =(2πr)2.
So, Area of circle : Area of Square
=πr2:(2πr)2=π4=7224=1114