To solve the problem step by step, we will follow these calculations:
### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid is given by the formula:
\[
V = \text{length} \times \text{breadth} \times \text{height}
\]
Given dimensions are:
- Length = 72 cm
- Breadth = 30 cm
- Height = 75 cm
Substituting the values:
\[
V = 72 \, \text{cm} \times 30 \, \text{cm} \times 75 \, \text{cm}
\]
Calculating the volume:
\[
V = 72 \times 30 = 2160 \, \text{cm}^2
\]
\[
V = 2160 \times 75 = 162000 \, \text{cm}^3
\]
### Step 2: Calculate the Volume of One Cube
The volume \( V_c \) of a cube is given by the formula:
\[
V_c = \text{edge}^3
\]
Given edge of the cube = 6 cm.
Calculating the volume of one cube:
\[
V_c = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} = 216 \, \text{cm}^3
\]
### Step 3: Calculate the Number of Cubes Formed
To find the number of cubes formed, we divide the volume of the cuboid by the volume of one cube:
\[
\text{Number of cubes} = \frac{\text{Volume of cuboid}}{\text{Volume of one cube}} = \frac{162000 \, \text{cm}^3}{216 \, \text{cm}^3}
\]
Calculating the number of cubes:
\[
\text{Number of cubes} = 750
\]
### Step 4: Calculate the Surface Area of One Cube
The surface area \( A \) of a cube is given by the formula:
\[
A = 6 \times \text{edge}^2
\]
Calculating the surface area of one cube:
\[
A = 6 \times (6 \, \text{cm})^2 = 6 \times 36 \, \text{cm}^2 = 216 \, \text{cm}^2
\]
### Step 5: Convert Surface Area to Square Meters
To convert square centimeters to square meters, we divide by \( 10000 \):
\[
A = \frac{216 \, \text{cm}^2}{10000} = 0.0216 \, \text{m}^2
\]
### Step 6: Calculate the Total Surface Area of All Cubes
The total surface area of all cubes formed is:
\[
\text{Total Surface Area} = \text{Number of cubes} \times \text{Surface Area of one cube}
\]
Calculating the total surface area:
\[
\text{Total Surface Area} = 750 \times 0.0216 \, \text{m}^2 = 16.2 \, \text{m}^2
\]
### Step 7: Calculate the Cost of Polishing
The cost of polishing is given as Rs 150 per square meter. Therefore, the total cost \( C \) is:
\[
C = \text{Total Surface Area} \times \text{Cost per square meter}
\]
Calculating the cost:
\[
C = 16.2 \, \text{m}^2 \times 150 \, \text{Rs/m}^2 = 2430 \, \text{Rs}
\]
### Final Answer
The number of cubes formed is **750** and the cost of polishing the surface of all the cubes is **Rs 2430**.
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