Question

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)

Answer 1

The carton is 3x6.6 x 2*6.6 cm^2

the cans have an area of 6*PI*3.3^2

Answer 2

answer should be in percent

Answer 3

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%

Answer 4

thanks