Problema Solution
Between Shangri-La and Xanadu ther is a mountain of granite (density= 1.60x10^2lb/ft^3) It is 1.00mi^3 in volume. Fate has decreed that a certain family of birds send one of their flock once in every one-hundred years (1.00x10^2) to sharpen its beak by rubbing it on the mountain. In this proccess, one-tenth of a milligram(1.00x10^-1mg) of the mountain is worn away each time. How many years will it take to wear away the entire mountain?
Answer provided by our tutors
first we will find the mass of the mountain using the formula:
mass = density*volume
density= 1.60*10^2 lb/ft^3
volume = 1.00 mi^3
1 mi = 5280 ft
1 mi^3 = 5280^3 ft^3
volume = 5280^3 ft^3
mass = 1.60 *10^2 * 5280^3
mass = 2355167232*10^4 lbs
1 lbs = 453592 mg
mass = 2355167232*10^4/453592 mg
mass = 5192.2692933*10^4 mg
one-tenth of a milligram(1.00x10^-1mg) of the mountain is worn every 100 years
(5192.2692933*10^4 : 1.00x10^-1)*1.00x10^2 = 5192.2692933*10^5*1.00x10^2 = 5192.2692933*10^7 years = 51,922,692,933 years