To give a more detailed breakdown:

Sugar Density and Weight-to-Volume Conversion:

1. • The weight-to-volume conversion for sugar is based on its density. Since sugar granules have a specific weight per unit volume, we can calculate how many cups are in one pound. 
     • • • Granulated Sugar:
           • 1 cup of granulated sugar weighs about 7 ounces.
           • Since 1 pound equals 16 ounces, you can divide the weight of a pound (16 ounces) by the weight of 1 cup (7 ounces) to get the number of cups.

           7 ounces per cup 16 ounces ​ =2.2857 cups
           This means that 1 pound of granulated sugar is approximately 2 1/4 cups.

           Other Types of Sugar:

           • Powdered Sugar (Confectioner’s Sugar): This sugar is lighter because it’s finely powdered. Typically, 1 pound of powdered sugar is about 3 1/2 to 4 cups. The volume can vary slightly based on how it’s sifted.
           • Brown Sugar (packed): Brown sugar, when packed into a measuring cup, weighs a bit more than granulated sugar. One pound of packed brown sugar is about 2 1/3 cups.

Why the Difference?

• Granulated sugar has a relatively consistent density because the crystals are compact, but brown sugar contains molasses, and powdered sugar is finely ground and airy. These factors influence how much volume a pound of each will occupy.

To summarize:

• Granulated Sugar: 1 pound ≈ 2 1/4 cups
• Powdered Sugar: 1 pound ≈ 3 1/2 to 4 cups
• Brown Sugar (packed): 1 pound ≈ 2 1/3 cups

This should give you a detailed understanding of how many cups are in one pound of different types of sugar!