A large cube is formed from the material obtained by melting 3 cubes of sides 3 units, 4 units and 5 units. What is the ration of the sum of the total surface area of the small cubes to that of the large cubes?
A. 1:1
B. 12:7
C. 25:18
D. 12:13
E. 12:17
Melting cube!
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Total volume of all 3 cubesvinay1983 wrote:A large cube is formed from the material obtained by melting 3 cubes of sides 3 units, 4 units and 5 units. What is the ration of the sum of the total surface area of the small cubes to that of the large cube?
A. 1:1
B. 12:7
C. 25:18
D. 12:13
E. 12:17
(3x3x3) + (4x4x4) + (5x5x5) = 27 + 64 + 125 = 216
So, the NEW cube must have volume of 216 cubic units
If we let k be length of one side of NEW cube, then we know that k^3 = 216
Solve, to get k = 6
So, the NEW cube has dimensions 6x6x6
Total surface of the 3 original cubes
6(3x3) + 6(4x4) + 6(5x5) = 6(9) + 6(16) + 6(25)
= 6(50)
Total surface of the NEW cube
6(6x6) = 6(36)
The ratio of total surface area of the small cubes to that of the NEW cube = 6(50)/6(36)
= 50/36
= [spoiler]25/18[/spoiler]
= C
Cheers,
Brent
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Why do you do 6(old cube surface)+6(old cube surface)+^(old cube surface)?
Why is it 6?? When 6 is the side of the new big cube?
Why is it 6?? When 6 is the side of the new big cube?
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A cube has 6 faces, so if the length of one edge of a cube is k, each of the six faces has area k^2, and the total surface area of the cube is 6k^2.shefdsouza wrote:Why do you do 6(old cube surface)+6(old cube surface)+^(old cube surface)?
Why is it 6?? When 6 is the side of the new big cube?
So the number '6' appears in the solution to this problem for two completely different reasons -- you'll always multiply by 6 when you calculate the surface area of any cube, but in this question '6' coincidentally also happens to be the length of an edge of the largest cube.
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I'm not sure about the stem here: it's not clear whether the cube is made by gluing the cubes together in some way (like a tower of cubes) or by breaking in down into 216 unit cubes, then using those to form a giant cube. I guess the intention is the second ... but even then 'melting' gives such a strange (and wrong) impression of what's happening here.
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If we picture the cubes being made out of some metal or plastic that can be melted into liquid state, then poured into a new mold without changing total volume, this could make sense.Matt@VeritasPrep wrote:I'm not sure about the stem here: it's not clear whether the cube is made by gluing the cubes together in some way (like a tower of cubes) or by breaking in down into 216 unit cubes, then using those to form a giant cube. I guess the intention is the second ... but even then 'melting' gives such a strange (and wrong) impression of what's happening here.
Ceilidh Erickson
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