piyush_nitt wrote:manish_shr wrote:A cube of white chalk is painted red, and then cut parallel to a pair of parallel sides to form two rectangular solids of equal volume. What percent of the surface are of each of the new solids is not painted red?
a. 15%
b. 16(2/3)%
c. 20%
d. 25%
e. 33(1/3)%
i always end up getting 25% but thats not the OA. Can anyone plz explain this one?
IMO E
side of a cube = a (say)
surface area of each cube = 3a^2(6a^2/2)
on partition , 5 sides of the new rectangular block has to be painted.
therefore area of remaining side is a^2
hence %age = a^2/3a^2 = 1/3 = 33.33
No dear! You are at error if you think that when a cube is cut into equal halves in the fashion as given in the question, the surface area of each smaller part becomes half of the big one; this in fact happens to its volume. See what happens:
If 'a' was each side of the original cube, then the new rectangular solid so formed would have its dimensions as 'a by a by a/2'; and only one square face (i.e. a * a = a ^ 2) will remain unpainted out of the total surface area, which is 2 [a * a + a * a/2 + a * a/2] = 4 a ^ 2, leaving the unpainted part's percentage = [(a ^ 2)/(4 a ^ 2)] * 100 = 25%.
So my answer is 'd'.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
This is really very pathetic elucidation to the problem.
