Question

If a wire of 440m length is moulded in the form of a circle and a square turn by turn, find the rayio of the area of the circle yo that of square.

Answer 1

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

Answer 2

Given, Length of wire = 440m.

(i) Circle:

We know that Perimeter of circle = 2πr

⇒ 2πr = 440

⇒ πr = 220 cm.

⇒ r = 220 * 7/22

⇒ r = 70 m.

∴ Area of circle = πr²

                          = (22/7) * (70)²

                          = 15400 m²

(ii) Square:

We know that Perimeter of square = 4s.

⇒ 4s = 440

⇒ s = 110

∴ We know that Area of square = s²

                                                     = (110)²

                                                     = 12100 m²

Now,

Ratio of circle : square

⇒ 15400/12100

⇒ 154/121

⇒ 14/11

⇒ 14:11.

Therefore,Ratio of area of the circle to that of square = 14:11.

Hope it helps!