To solve the problem step by step, we will follow the reasoning laid out in the video transcript.
### Step 1: Calculate the volume of the large cube
The edge length of the large cube is given as 1 meter. The volume \( V \) of a cube is calculated using the formula:
\[
V = \text{edge}^3
\]
So, the volume of the large cube is:
\[
V_{\text{large}} = 1^3 = 1 \, \text{m}^3
\]
### Step 2: Calculate the volume of the small cube
The edge length of the small cube is given as \( 1 \, \mu m \) (micrometer), which is equal to \( 1 \times 10^{-6} \, m \). Thus, the volume of the small cube is:
\[
V_{\text{small}} = (1 \times 10^{-6})^3 = 1 \times 10^{-18} \, \text{m}^3
\]
### Step 3: Determine the number of small cubes
To find out how many small cubes can be made from the large cube, we divide the volume of the large cube by the volume of a small cube:
\[
\text{Number of small cubes} = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{1 \, \text{m}^3}{1 \times 10^{-18} \, \text{m}^3} = 10^{18}
\]
### Step 4: Calculate the surface area of one small cube
The surface area \( A \) of a cube is given by the formula:
\[
A = 6 \times \text{side}^2
\]
For the small cube:
\[
A_{\text{small}} = 6 \times (1 \times 10^{-6})^2 = 6 \times 1 \times 10^{-12} \, \text{m}^2 = 6 \times 10^{-12} \, \text{m}^2
\]
### Step 5: Calculate the total surface area of all small cubes
The total surface area \( A_{\text{total}} \) of all the small cubes is the surface area of one small cube multiplied by the number of small cubes:
\[
A_{\text{total}} = A_{\text{small}} \times \text{Number of small cubes} = 6 \times 10^{-12} \, \text{m}^2 \times 10^{18} = 6 \times 10^{6} \, \text{m}^2
\]
### Step 6: Express the total surface area in terms of \( n \)
According to the problem, the total surface area is given as \( n \times 100000 \, \text{m}^2 \):
\[
6 \times 10^{6} = n \times 10^{5}
\]
### Step 7: Solve for \( n \)
To find \( n \), we rearrange the equation:
\[
n = \frac{6 \times 10^{6}}{10^{5}} = 6 \times 10^{1} = 60
\]
Thus, the value of \( n \) is \( 60 \).
### Final Answer
The value of \( n \) is \( 60 \).
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