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?

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?

• A. 502.65 in²
• B. 1005.31 in²
• C. 402.12 in²
• D. 1200 in²

Answer: (B)

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):

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):