cube problem

**ags_uber** · 08-09-2008, 08:15 AM

Four cubes of same size were placed on the top of another four cubes of similar size to form a rectangular solid. Exactly one face of each cube was pained with blue.
What is the greatest fraction of the total surface area of the solid that could be blue?

(A) 1/6
(B) 3/14
(C) 1/4
(D) 2/7
(E) 1/3

**ags_uber** · 08-09-2008, 08:19 AM

the answer is supposed to be 1/3 but can anyone explain hw..

**chestnut.cc** · 08-09-2008, 08:50 AM

Four cubes of same size were placed on the top of another four cubes of similar size to form a rectangular solid. Exactly one face of each cube was pained with blue.
What is the greatest fraction of the total surface area of the solid that could be blue?

(A) 1/6
(B) 3/14
(C) 1/4
(D) 2/7
(E) 1/3

Let the side of the cube be 1... Then calculate the area of the blue faces... then calculate the dimensions and area of the cuboid... if the cuboid is rectangular there is only 1 possible arrangement of 4 cubes on top of 4 cubes... ie 2*4*1... calc the total surface area of the solid... then the greatest fraction will be when all the blue faces are visible... The total surface area of the blue faces is 8*1... ie 8... the total surface area of the cuboid is 2(2*1+8*1+4*1)... ie 28... the greatest fraction that could be blue is 8/28... 2/7... D

**mewidyu** · 08-09-2008, 10:28 AM

one side of the cube has 4 faces so there will be total of 24 faces but as there are only 8 cubes total so the only 8 faces will be blue in color...
if all the blue color faces are on the surface then the fraction will be 8/24 i.e. 1/3

**scaredOfQuant** · 08-09-2008, 11:21 AM

mewidyu , The solid formed is a cuboid. Total surface area of the cuboid should be taken into consideration while solving this prolem, not 8 times the surface area of individual cube. If you solve this way you will get 2/27. May be I am misinterpreting the question.

**mewidyu** · 08-09-2008, 11:45 AM

ok..
if yu want to solve it this way then assume each side of the small cube is a then the area of the one side will be a^2 so the area of all blue painted surface will be 8a^2...
and the total surface area of the cuboid will be 24a^2.
if all the surface painted in blue facing outside then the fraction will be 8a^2/24a^2 ... hence the answer will be 1/3..........

**mewidyu** · 08-09-2008, 11:47 AM

the total surface area of the cuboid when all blue painted surface are facing out will be 24 only....

**chestnut.cc** · 08-09-2008, 11:49 AM

no dude... the only possible cuboid you can make has dimensions 2*4*1... surface area 28...

**mewidyu** · 08-09-2008, 12:07 PM

Originally Posted by chestnut.cc

no dude... the only possible cuboid you can make has dimensions 2*4*1... surface area 28...

ok.. can yu explain it again...
i m not getting it....

thanx.

**chestnut.cc** · 08-09-2008, 01:36 PM

there are two poss ways of placing 4 cubes on top of 4 cubes... either you make another cube... or you place them lengthwise... since were told the solid is a cuboid... the only poss arrangement is the second case...