A popcorn company needs to print a label for a can with a diameter of 16 inches and a height of 20 inches. How much surface area does the label cover?

To determine the surface area that the label covers on a cylindrical can, you'll want to calculate the lateral surface area of the cylinder. The formula for the lateral surface area ( A ) of a cylinder is given as:

[ A = 2 \pi r h

]

where ( r ) is the radius and ( h ) is the height of the cylinder.

First, since the diameter of the can is 16 inches, the radius ( r ) would be half of that:

[ r = \frac{16}{2} = 8 \text{ inches} ]

The height ( h ) is provided as 20 inches. Substituting these values into the formula gives:

[ A = 2 \pi (8)(20) ]

Calculating it step-by-step:

1. Multiply the radius by the height: ( 8 \times 20 = 160 ).

2. Then multiply by ( 2\pi ): [ A = 2 \pi \times 160 = 320\pi ]

3. To get a numerical value, use an approximation for ( \pi ) (around 3.14):