The Little Can Company makes cylindrical cans with a height of 3 inches and radius of 1 inch. The entire lateral face is covered by a label. The paper for the labels is purchased in rolls 3 inch high. When unrolled the paper is 10 yards long. How many labels can be made from each roll, assuming the label does not overlap on the can?
the circumference if the can is 2π.
So, there are
10*36/2π labels per roll
To determine how many labels can be made from each roll, we need to calculate the total area of the labels and the area of each label.
First, let's calculate the area of a single label. The label covers the lateral face of the can, which can be thought of as the curved surface of a cylinder. The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height. For the given can, the radius is 1 inch and the height is 3 inches.
A = 2π(1)(3)
= 6π square inches
Now, let's determine the area of the labels that can be made from the 10-yard-long roll, which is equivalent to 360 inches. Since the labels are 3 inches high, we can calculate the width of each label by dividing the total length of the paper (360 inches) by the height of each label (3 inches).
Width of each label = Total length of paper / Height of each label
= 360 inches / 3 inches
= 120 inches
Therefore, each label has an area of 120 square inches (height of 3 inches multiplied by width of 120 inches).
Now, we can calculate the number of labels that can be made from the roll by dividing the total area of the roll by the area of each label.
Number of labels = Total area of roll / Area of each label
= 360 inches / 120 square inches
= 3
Therefore, three labels can be made from each roll, assuming the label does not overlap on the can.