Melting cube!

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vinay1983 Legendary Member
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Melting cube!

Post Mon Sep 30, 2013 6:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    Post Mon Sep 30, 2013 7:07 am
    vinay1983 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
    Total volume of all 3 cubes
    (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
    = 25/18
    = C

    Cheers,
    Brent

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