A peanut manufacturing company pays $0.02 per square inch of label used on its cylindrical peanut containers. Each container has a radius of 1.5 inches and a height of 2.5 inches. If the label covers the lateral area of the container, how much would it cost to produce 150,000 labels?
c. $52,988
cost=.03*1.5*2PI*2.5*150,000
$3,000
B. $11,250
C. $52,988
D. $70,650
To find out how much it would cost to produce 150,000 labels, we first need to calculate the total surface area of each cylindrical container.
The lateral area of a cylinder can be calculated using the formula:
Lateral Area = 2 * π * r * h
In this case, the radius, r, is 1.5 inches and the height, h, is 2.5 inches. Substituting these values into the formula:
Lateral Area = 2 * π * 1.5 * 2.5
= 7.5π square inches
Since the label covers the entire lateral area of the container, the surface area of the label is 7.5π square inches.
Now we can calculate the cost per label. The company pays $0.02 per square inch of label used. Therefore, the cost per label is:
Cost per label = 7.5π square inches * $0.02/square inch
= 0.15π dollars
Finally, we can calculate the total cost of producing 150,000 labels:
Total cost = Cost per label * Number of labels
= 0.15π dollars/label * 150,000 labels
≈ 70,680 dollars
So, it would cost approximately $70,680 to produce 150,000 labels for the peanut manufacturing company.