Expert: Abe Mantell - 8/28/2010

Question
Hi im a student of engineering and ive come across this problem that has me stumped

a manufacturer receives an order for 2000 souvenirs which are to be miniature models of the Washington monument, each must be exactly similar to the original monument and must be 4 in. high. if the models are solid, find the amount of material necessary to fill the order. (take 1,038,800 cu. ft. as volume of Washington Monument, 555ft in height)

Answer
Let's look at the ratio of heights.
555 ft vs 4 inches...4 inches is 1/3 of a ft, so we have
555/(1/3) = 1665...so the actual monmument is 1665 times bigger
in all its linear measurements (i.e. 1665 times taller, 1665 times
as wide, and 1665 times as deep)...thus, it is 1665^3 times the
volume...sooooo, the souvenir will be 1/1665^3 the volume of the
actual monument ==> (1,038,800 cu. ft.)/(1665^3) just for one
souvenir...2000 of them would have a volume of
2000*(1,038,800 cu. ft.)/(1665^3) = (about) 0.45 cu. ft.

Abe