twelve cans, each 6.6 cm in diameter are packed into a carton.
what is the efficiency of this package; that is, what percent of the total base area of the carton is covered by the cans? (use the formula A = πr^2 to calculate the area of a circle)
The carton is 3x6.6 x 2*6.6 cm^2
the cans have an area of 6*PI*3.3^2
answer should be in percent
The cans can be packed as 3 by 4, 2 by 6 , or 1 by 12
If stored as 3 by 4:
length of base = 4(6.6) or 26.4 cm
width of base = 3(6.6) or 19.8
area of base = (26.4)(19.8) cm^2
= 522.72 cm^2
Note that the area of the base for the other cases would be the same.
e.g. (2)(6.6)(6)(6.6) = 522.72
area of 12 cans = 12(π(3.3)^2) = appr 410.54 cm^2
Percentage of base covered = 410.54/522.72(100)% = 78.5%
thanks
To find the efficiency of this package, we need to calculate the total base area covered by the twelve cans and then express it as a percentage of the total base area of the carton.
First, let's calculate the area of one can using the formula A = πr^2, where r is the radius of the can:
Given: Diameter of each can = 6.6 cm
Radius (r) = Diameter / 2 = 6.6 cm / 2 = 3.3 cm
Now, we can calculate the area (A) of one can:
A = π(3.3 cm)^2
A ≈ 34.21 cm^2 (rounded to 2 decimal places)
Since there are twelve cans, the total area covered by them will be:
Total area covered = 12 x 34.21 cm^2
Total area covered ≈ 410.52 cm^2 (rounded to 2 decimal places)
To find the efficiency, we need to express the total area covered by the cans as a percentage of the total base area of the carton.
Since the cans are circular and packed into a carton, the base area of the carton will be a rectangle with dimensions equal to the length and width of the carton. However, since the dimensions of the carton are not given in the question, we cannot directly calculate the base area. Therefore, we cannot determine the exact percentage efficiency in this case without that information.
If you have the dimensions of the carton (length and width), you can calculate the base area and then use the formula:
Efficiency (%) = (Total area covered / Base area of carton) x 100
Please provide the dimensions of the carton if you have them, and I can help you calculate the efficiency.