A cylinder of curved surface area 1250m² is formed from a rectangular metallic sheet .Find the dimensions of the rectangular sheet I its length is double its breadth?

To find the dimensions of the rectangular sheet, we'll first need to calculate the height and the radius of the cylinder.

1. Start by determining the length and breadth of the rectangular sheet.
Let the breadth be x.
Since the length is double the breadth, the length is 2x.

2. Calculate the height of the cylinder.
To find the height, we can use the formula for the curved surface area of a cylinder: CSA = 2πrh, where CSA is the curved surface area, π is approximately 3.14159, r is the radius, and h is the height.
Given that the curved surface area is 1250 m², we can rewrite the formula as 1250 = 2πrh.

3. Calculate the radius of the cylinder.
Since the rectangular sheet is rolled up to form the cylinder, the length of the rectangular sheet becomes the circumference of the base of the cylinder.
Circumference = 2πr, where r is the radius.
Given that the length is 2x, the circumference is 2πr = 2x.
Dividing both sides by 2π, we get r = x/π.

4. Substitute the value of r into the equation for the curved surface area.
1250 = 2π(x/π)h.
Simplify by canceling out π on both sides: 1250 = 2xh.
Divide both sides by 2x to solve for h: h = 1250/(2x) = 625/x.

5. Solve for the values of x and 2x.
We have two equations from steps 2 and 4:
Equation 1: h = 625/x
Equation 2: h = 2x

Since both equations equal h, we can set them equal to each other: 625/x = 2x.
Multiply both sides by x to get rid of the fraction: 625 = 2x^2.
Divide both sides by 2: 312.5 = x^2.
Taking the square root of both sides, we get x = √312.5 = 17.68 (approx).
Therefore, the breadth of the rectangular sheet is approximately 17.68 meters.

To find the length, we can substitute x into the equation for the length: 2x = 2(17.68) = 35.36 meters.
Therefore, the length of the rectangular sheet is approximately 35.36 meters.

So, the dimensions of the rectangular sheet are approximately 35.36 meters (length) and 17.68 meters (breadth).

w*2w = 1250

Now get w, then the length is 2w