Problem 1
Answer: Lateral area
Explanation:
The word "lateral" means "side", which I tend to think of as the wall. This is in contrast to the floor and ceiling faces which are circles.
The total surface area is not considered because we aren't including the circular faces.
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Problem 2
Answer: lateral surface area = 2*pi*r*h
Explanation:
Imagine peeling the label off the can. It unrolls to form a rectangle (assuming no cuts or tears happen). Check out the set of diagrams below to get an idea of how this unfolding process happens.
This rectangle has the same height as the cylinder. The horizontal component is the circumference of the can.
lateral area = (length)*(height)
lateral area = (circumference)*(height)
lateral area = (2pi*r)*(h)
lateral area = 2*pi*r*h
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Problem 3
Answer: Approximately 75.36 square inches
Work Shown:
r = radius = 2 inches (half of the 4 inch diameter)
h = height = 6 inches
LSA = lateral surface area = area of the label
LSA = 2pi*r*h
LSA = 2*3.14*2*6
LSA = 75.36