Let k be a given measure of length; then suppose a cubic particle of dimension 3
ID: 521145 • Letter: L
Question
Let k be a given measure of length; then suppose a cubic particle of dimension 3k times 3k times 3k is split up into 27 cubes of size k times k times k. Calculate the relative increase in surface area when this occurs by comparing the surface area (length times width) of the six faces of the larger cube to the sum of all those of the smaller ones. From your answer, deduce whether the total surface area of a given mass of atmospheric particle is larger or smaller when it occurs as a large number of small particles rather than a small number of large ones.Explanation / Answer
surface area of cube=6*(side)^2
surface area for the original cube=6*(3k)^2=54k^2
Surface area of smaller cubes formed=6k^2
Total surface area of 27 small cubes=27*6*k^2=162k^2
relative increase in surface area=(increase in surface area/original surface area)*100=(162k^2-54k^2)*100=200%
the total surface area of large number of small particles is larger than that of small number of large ones
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.