Final answer:
When scaling the dimensions of a cylindrical container by a factor of 2, the new length and diameter are calculated by multiplying the original dimensions by 2, resulting in a family-size container that is 10 inches long and 8 inches in diameter.
Step-by-step explanation:
In scaling the dimensions of a cylindrical container by a factor of 2, where the original container has a length of 5 inches and a diameter of 4 inches, applying the scale factor yields the following:
New Length = Original Length × Scale Factor = 5 inches × 2 = 10 inches
New Diameter = Original Diameter × Scale Factor = 4 inches × 2 = 8 inches
Hence, the dimensions of the family-size product are a length of 10 inches and a diameter of 8 inches. Scaling dimensions by a factor of 2 essentially doubles each dimension, maintaining the proportional relationships within the cylindrical shape. This information is vital for various applications, such as packaging design, where understanding the scaled dimensions helps ensure accurate sizing for manufacturing and storage purposes.