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?

Question

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calculista calculista · Answer 1 · 2020-01-07T13:13:14+01:00

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]