Final answer:
The radius of the cylinder formed by rolling a rectangular sheet of paper with a width of 22 cm is approximately 3.5 cm, calculated by equating the circumference of the circle to the width of the paper and solving for the radius.
Step-by-step explanation:
To find the radius of the cylinder formed by rolling a rectangular piece of paper, we can equate the circumference of the cylinder's base to the length of the paper lying along the roll. In this case, the paper has a length of 40 cm, which will be the height of the cylinder, and a width of 22 cm, which will become the circumference of the base of the cylinder.
Using the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius, we can solve for r by setting the circumference equal to the width of the paper:
C = 2πr = 22 cm
Solving for the radius r, we get:
r = C / (2π)
r = 22 cm / (2 * 3.1415927...)
r = 22 cm / 6.2831854...
r ≈ 3.5 cm
So, the radius of the cylinder is approximately 3.5 cm.