Final answer:
To cover the side of the can with a paper label, 20π square inches of paper is needed. The can can hold 20π cubic inches of soup.
Step-by-step explanation:
To determine how much paper is needed to cover the side of the can, we need to find the surface area of the side of the can. The side of the can is in the shape of a cylinder, so we can use the formula for the lateral surface area of a cylinder:
LSA = 2πrh
Given that the can has a height of 5 inches and a base diameter of 4 inches, we can find the radius (r) by dividing the diameter (4 inches) by 2, which gives us 2 inches. Substituting the values into the formula, we have:
LSA = 2π(2 inches)(5 inches) = 20π inches^2
Therefore, we need 20π square inches of paper to cover the side of the can.
To determine how much soup will fit in the can, we need to find the volume of the can. Again, we can use the formula for the volume of a cylinder:
V = πr^2h
Substituting the values we already know, we have:
V = π(2 inches)^2(5 inches) = 20π cubic inches
Therefore, the can can hold 20π cubic inches of soup.