A steel wire,when bent to form a square encloses an area of 484cmsq. If the same wire is bent to form a circle,find the area of the circle.
Gve me ful sltn plz
nd ans is 616cmsq.
To find the area of the circle, we need to know the length of the wire. Let's start by finding the length of the wire required to form the square.
Since a square has four sides of equal length, let's assume the length of one side of the square as 's'. The perimeter of the square is given by the formula: P = 4s.
The length of the wire is the same as the perimeter of the square. So, the perimeter of the square is given as 4s = length of the wire.
Given that the enclosed area of the square is 484 square cm, we can find the length of one side of the square.
Area of square = side^2
484 = s^2
Taking the square root of both sides, we get:
s = sqrt(484) = 22 cm (taking the positive value only, as side length cannot be negative).
Now, we have the length of one side of the square. To find the perimeter of the square (length of the wire), we multiply the side length by 4:
P = 4s = 4 * 22 = 88 cm (length of the wire).
Now, let's find the area of the circle using the length of the wire.
The perimeter of the circle (length of the wire) is equal to the circumference of the circle (C). The formula for the circumference of a circle is given by:
C = 2πr, where r is the radius of the circle.
Now, we need to find the radius of the circle using the given length of the wire (88 cm).
C = length of the wire = 2πr
88 = 2πr (substituting the value of C)
Dividing both sides by 2π, we get:
r = 88 / (2π) = 14 cm (approximated to two decimal places).
Now, we have the radius of the circle (r = 14 cm). We can use the formula for the area of a circle to find the area.
Area of the circle = πr^2
Area = π * (14)^2 = π * 196 = 616 cm^2
Hence, the area of the circle formed by the steel wire is 616 cm^2.
each side of square --- x
x^2 = 484
x = 22
So now the circumference = 88
2πr = 22
r = 44/π
area = π(44/π)^2 = 1936/π = appr 616.2