Mathematics

Question

How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?
How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

1 Answer

  • Answer:

    Part 3) [tex]SA=288\ cm^2[/tex]

    Part 4) [tex]64\ cm^2[/tex]

    Step-by-step explanation:

    Part 3) Calculate the total surface area of three 4 cm cubes

    we know that

    The surface area of a cube is equal to the area of its six square faces

    [tex]SA=6b^2[/tex]

    so

    The surface area of three cubes is equal to the area of its 18 square faces

    [tex]SA=18b^2[/tex]

    where

    b is the length side of the square face

    In this problem

    [tex]b=4\ cm[/tex]

    so

    The surface area of three cubes is

    [tex]SA=18b^2[/tex]

    substitute the given value

    [tex]SA=18(4)^2[/tex]

    [tex]SA=288\ cm^2[/tex]

    Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

    In this case the total surface area of the three glued 4-cm cubes is equal to the area  of  its 14 square faces

    so

    The surface area lost is equal to

    [tex]18b^2-14b^2=4b^2[/tex]

    substitute

    [tex]4(4)^2=64\ cm^2[/tex]

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