To find the volume of the cylinder formed by folding a rectangular piece of paper measuring 11 cm by 4 cm without overlapping, we first need to determine the dimensions of the cylinder.
The height of the cylinder is given as 4 cm. Since the paper is folded along the longer side, we can assume that the circumference of the base of the cylinder will be equal to the remaining length of the paper, which is 11 cm.
We know that the circumference (C) of a circle is given by the formula:
C = 2πr
Where r is the radius of the cylinder’s base. Setting the circumference equal to 11 cm, we have:
2πr = 11
Now, we can solve for r:
r = 11 / (2π) ≈ 1.75 cm
Next, we can calculate the volume (V) of the cylinder using the formula:
V = πr²h
Substituting the values we have:
V = π(1.75)²(4)
V ≈ π(3.0625)(4) ≈ π(12.25) ≈ 38.48 cm³
Therefore, the volume of the cylinder formed by folding the rectangular piece of paper is approximately 38.48 cm³.