What is the volume of a cylinder formed by folding an 11cm by 4cm piece of paper without overlapping, resulting in a height of 4cm?

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Calculating the Volume of the Cylinder

To determine the volume of the cylinder created by folding a rectangular piece of paper measuring 11 cm by 4 cm, we begin by identifying the dimensions of the cylinder.

Step 1: Understanding the Cylinder’s Dimensions

When the paper is folded, the height (h) of the cylinder is given as 4 cm.

Since the height remains consistent with one of the dimensions of the paper, we will calculate the circumference of the base of the cylinder using the remaining length of the paper.

Step 2: Finding the Cylinder’s Radius

The circumference (C) of the base of the cylinder can be derived from the length not used for the height:

C = 11 cm

Using the relation between the circumference and radius (r):

C = 2 * π * r

We can substitute and solve for the radius:

11 cm = 2 * π * r

Solving for r: 

r = 11 cm / (2 * π) ≈ 1.75 cm

Step 3: Calculating the Volume

The formula for the volume (V) of a cylinder is given by:

V = π * r² * h

Substituting the values of the radius and height:

V = π * (1.75 cm)² * 4 cm

This simplifies to:

V ≈ π * 3.0625 cm² * 4 cm ≈ 12.25π cm³

Calculating the final volume using the value of π ≈ 3.14:

V ≈ 12.25 * 3.14 cm³ ≈ 38.48 cm³

Conclusion

Thus, the volume of the cylinder formed by folding the paper is approximately 38.48 cm³.

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