Question

1. you are making your own salsa and placing it into jars for sale at a local farmers market. you want to make a label to wrap around the jars. the jars are cylindrical with a diameter of 4\ and a height of 3\. what should the dimensions of the rectangular labels be if they are to wrap all the way around the jar?

explain your thinking.

Explanation:

Identify the given dimensions

We are given a cylindrical jar with:

• Diameter \(d = 4\text{ inches}\)
• Height \(h = 3\text{ inches}\)

Relate label to cylinder net

Using the Circumference of a Circle concept, wrapping a rectangular label around a cylinder means:

• The height of the label matches the cylinder's height.
• The length of the label matches the cylinder's circumference.

Calculate the label length

Using the Circumference Formula Application and Diameter and Radius concepts:

$$ C = \pi \cdot d $$

$$ C = 4\pi \approx 12.57\text{ inches} $$

State the final dimensions

The rectangular label must have:

• Height = \(3\text{ inches}\)
• Length = \(4\pi\text{ inches}\) (approximately \(12.57\text{ inches}\))

Answer:

The dimensions of the rectangular label should be \(3\text{ inches}\) by \(4\pi\text{ inches}\) (approximately \(12.57\text{ inches}\)).