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A roll of tape is on a spool with diameter 3.6 cm. The diameter of the spool plus the diameter
of the tape is 5.4 cm. The tape is 25.4 m long. The number of layers on the tape is closest to
a) 160
b) 180
c) 215
d) 230
e) 1773
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The minimum diameter (the diameter of the first layer) is d = 3.6 cm;
the circumference (the length) of the first layer is = 3.14159*3.6 = 11.309724 cm.
The maximum diameter (the diameter of the last layer) is D = 5.4 cm;
the circumference (the length) of the last layer is = 3.14159*5.4 = 16.964586 cm.
The lengths of consecutive layers make an arithmetic progression with the common difference ,
where is the thickness of the tape. Therefore, the number of layers n can be found from
the formula of the sum of an arithmetic progression
2540 = = = 14.137155*n,
n = = 179.67 (approximately).
ANSWER. The number of layers on the tape (approximately 180), is closest to option b).
Solved.