If a wire of 440m length is moulded in the form of a circle and a square turn by turn, find the ratio of the area of the circle to that of square.
Answers
If a wire of 440 m length is molded in the form of a circle, total length of the wire will be equal to the total length( = circumference ) of the circle.
Now,
⇒ Circumference of the circle = total length of the wire
⇒ Circumference of the circle = 440 m
We know that the formula for the circumference of the circle is 2πr, where r is the radius of the circle.
Let the radius of this formed circle will be a,
Hence,
⇒ 2πa = 440 m
⇒ 2 x π x a = 440 m
⇒ 2 x ( 22 / 7 ) x a = 440 m
⇒ 44 / 7 x a = 440 m
⇒ a = 440 x 7 / 44 m
⇒ a = 10 x 7 m
⇒ a = 70 m
Now, radius of the circle is 70m.
Also, we know that the area of circle is πr^2, where r is the radius, so
⇒ Area of the circle = π x a^2
⇒ Area of the circle = ( 22 / 7 ) x ( 70 m )^2
⇒ Area of the circle = 22 x 10 x 70 m^2
⇒ Area of the circle = 15400 m^2
If a wire of 440 m length is molded in the form of a square, total length of wire will be equal to the perimeter of the square.
Now,
⇒ Perimeter of the square = 440m
We know that the perimeter of square is 4 a, where a is the side of the square.
Hence,
⇒ 4 x side of the square = 440 m
⇒ side of the square = 440 m / 4
⇒ side of the square = 110 m
We know that the area of square is side^2,
Hence,
⇒ Area of this square = ( 110 m )^2
⇒ Area of the square = 12100 m^2
Now,
⇒ Ratio of the area of the circle to the area of the square = ( 15400 m^2 ) : ( 12100 m^2 )
⇒ Ratio of the area of the circle to the area of the square = 154 : 121
⇒ Ratio of the area of the circle to the area of the square = 14 : 11
Therefore the ratio of the area of the circle to the area of the square is 14 : 11
Refer to attachment
