Question

a paper tube is formed by rolling a cardboard strip in a spiral and then gluing the edges together as shown in (figure 1). the paper is 2.2 mm thick and the tube has an outer diameter of 100 mm

Answer 1

The paper tube's inner diameter can be calculated by subtracting twice the paper thickness from the outer diameter. In this case, the inner diameter is
`\(100 \, \text{mm} - 2 * 2.2 \, \text{mm} = 95.6 \, \text{mm}.\)`

Step-by-step explanation:

To determine the inner diameter of the paper tube, we subtract twice the paper thickness from the outer diameter. The paper thickness is given as
`\(2.2 \, \text{mm},\)`so the inner diameter
`(\(D_{\text{inner}}\))` is calculated as follows:

`\[D_{\text{inner}} = D_{\text{outer}} - 2 * \text{thickness} = 100 \, \text{mm} - 2 * 2.2 \, \text{mm} = 95.6 \, \text{mm}.\]`

This calculation accounts for the fact that the paper tube is formed by rolling a cardboard strip in a spiral, and when the edges are glued together, the thickness of the paper is doubled. Therefore, the inner diameter of the tube is slightly smaller than the outer diameter.

Understanding these dimensions is crucial for various applications, such as designing packaging or calculating the volume of the tube. It ensures that accurate measurements are used for any further calculations or considerations related to the paper tube's properties.

In summary, the inner diameter of the paper tube is found by subtracting twice the paper thickness from the outer diameter, resulting in an inner diameter of
`\(95.6 \, \text{mm}.\)`