The task is to identify a date for the Chennai event which is a perfect cube and falls between the 5th October (Bengaluru event) and 15th October (Hyderabad event). Let's solve the problem step-by-step:
- First, find the range of dates between which the Chennai event must occur. The dates are from 6th October to 14th October inclusive.
- Next, we need to determine the perfect cubes that fall within this range. The cube of a number is obtained by multiplying the number by itself twice.
- Calculate the cubes of small integers and check if they fit within the date range:
- \(1^3 = 1\)
- \(2^3 = 8\)
- \(3^3 = 27\)
- \(4^3 = 64\)
- From the above calculations, we see that \(2^3 = 8\) is the only perfect cube that falls within the given date range (6th October to 14th October).
- Hence, the date for the Chennai event must be the 8th of October.
Therefore, the correct date for the Chennai event, which is a perfect cube between the given dates, is 8th October.
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