A cube with an edge length $4$ is divided into $8$ identical cubes. Calculate the difference between the combined surface area of the $8$ smaller cubes and the surface area of the original cube.

48

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56

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96

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288

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Solution

The correct option is C $96$
When a cube of length $4$ s divided into $8$ identical cubes, each cube has a length of $2$ .
So, $1$ cube of length $4$ is divided into $8$ smaller cubes of length $2$ .

Surface area of Cube of length $4$ will be $6 a^{2} = 6 \times 4^{2} = 96$
Surface area of smaller cube of length $2$ will be $6 a^{2} = 6 \times 2^{2} = 24$
Since there are $8$ cubes, the total surface area of all $8$ cubes will be $8 \times 24 = 192$
The difference between surface area of the $8$ smaller cubes and the surface area of the original cubes will be $192 - 96 = 96$

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Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

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A cube with an edge length 4 is divided into 8 identical cubes. Calculate the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube.

A cube with an edge length $4$ is divided into $8$ identical cubes. Calculate the difference between the combined surface area of the $8$ smaller cubes and the surface area of the original cube.