A rectangular sheet of metal with length 220 m and width 30 m is rolled along its length toform a cylinder. Find the volume of the cylinder thus formed.

Sure, here are the steps to find the volume of the cylinder:

Step 1: Understand the problem The rectangular sheet is rolled along its length to form a cylinder. This means that the length of the rectangle becomes the circumference of the base of the cylinder, and the width of the rectangle becomes the height of the cylinder.

Step 2: Find the radius of the base of the cylinder The formula for the circumference of a circle (which is the base of the cylinder) is C = 2πr, where C is the circumference and r is the radius. We know that the length of the rectangle, which is 220 m, is the circumference of the base of the cylinder. So, we can set up the equation 220 = 2πr and solve for r.

r = 220 / (2π) ≈ 35 m

Step 3: Find the volume of the cylinder The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base, h is the height, and V is the volume. We know that the radius of the base is approximately 35 m and the height is the width of the rectangle, which is 30 m.

So, V = π * (35 m)² * 30 m ≈ 116000 m³

So, the volume of the cylinder formed by rolling the rectangular sheet of metal is approximately 116000 cubic meters.