A square cake measures 6 units by 6 units by 4 units. The cake falls into a vat of frosting and comes out frosted on all 6 faces. The cake is then cut up into cubes, each measuring 1 unit on an edge. How many of these cubes will have exactly one face frosted?
2007-12-01 06:53:30 · 6 answers · asked by anonymous 2 in Science & Mathematics ➔ Mathematics
For "lithiumd's" info, it's not my opinion that this is a question for a genius. I got an email that was literally named the TEST OF GENIUS and this was serially question 3.
Thanks to everyone who answered.
2007-12-01 07:10:27 · update #1
The top & bottom of the cake would each have 4 * 4 pieces with one side frosted.
Each of the fours sides would have 4 * 2 pieces with one frosted side.
2 * 4 * 4 + 4 *4 * 2 = 64
2007-12-01 07:01:21 · answer #1 · answered by battleship potemkin AM 6 · 1⤊ 0⤋
Starting point: 6 x 6 x 4 = 144 cubes.
The only cubes with one frosted face are the cubes on the 6 surfaces but away from the edges of those surfaces. This is in effect two 4x4 (top and bottom, removing all edges) and four that are 4x2 (sides, removing all edges). This is 2 x 16 = 32 plus 4 x 4 x 2 = 32 for a total of 64.
All other cubes will have zero sides frosted (from the interior), two sides frosted (from the edges), or three sides frosted (at the corners.)
2007-12-01 07:03:47 · answer #2 · answered by The_Doc_Man 7 · 0⤊ 0⤋
This is hardly a "test of genius" problem. Just draw the cake and the answer is obvious.
The only cubes that have exactly one face frosted are those that formed a side of the initial cake, but did not form an edge.
There are two 6x6 sides, and four 6x4 sides of the initial cake.
The 6x6 sides each have 4x4 = 16 cubes that make up the side, but aren't part of the edge.
The 6x4 sides each have 4x2 = 8 cubes that make up the side, but aren't part of the edge.
So, the total number of cubes with one side frosted is
T = 16 + 16 + 8 + 8 + 8 + 8
T = 64
2007-12-01 06:59:13 · answer #3 · answered by lithiumdeuteride 7 · 2⤊ 0⤋
Is that really a genius problem - the answer's 64.. With a bit of thought!!
2007-12-01 07:08:55 · answer #4 · answered by Anonymous · 0⤊ 0⤋
6x6 faces: Interior pieces each: 4*4 = 16
4x6 faces: Interior pieces each: 2*4 = 8
There are 2 6x6 faces: 2 * 16 = 32
There are 4 4x6 faces: 4*8 = 32
32+32 = 64 pieces
2007-12-01 07:04:53 · answer #5 · answered by David D 2 · 1⤊ 1⤋
0 it's a square cake if you read the first 3 words
2014-04-12 15:10:28 · answer #6 · answered by Caroline 1 · 0⤊ 0⤋