Question

1a. How many years older will you be 1 giga-second from now? (Use 365 days make a year, without modification) b. Certain amounts of chemicals are being carefully diluted by gradually adding drops of water, one at a time. If the diameter of a drop of water is 2 mm., how many drops of water will you require to make of a 1.0-liter bottle?

Answer 1

a)

1 giga seconds = 10^9 seconds

1 hour = 3600 s

1 day = 3600*24 s

1 yr = 365*3600*24 s

So, 10^9 s = 10^9/(365*3600*24) = 31.71 years <------ answer

b)

Volume of 1 liter bottle = 1/1000 m3

Volume of drop of water = (4/3)*pi*d^3/8

= (4/3)*pi*(0.002)^3/8

= 4.19*10^-9 m3

So, number of drops needed = (1/1000)/(4.19*10^-9)

= 2.39*10^5 drops <------ answer