Find the volume and the surface area of a cuboid with dimensions:
length = 12 cm , breadth = 10 cm , height = 8 cm

Answer

To find the volume and surface area of a cuboid with the given dimensions, we will follow these steps:

### Step 1: Identify the dimensions of the cuboid
- Length (l) = 12 cm
- Breadth (b) = 10 cm
- Height (h) = 8 cm

### Step 2: Calculate the volume of the cuboid
The formula for the volume (V) of a cuboid is:
\[ V = l \times b \times h \]

Substituting the values:
\[ V = 12 \, \text{cm} \times 10 \, \text{cm} \times 8 \, \text{cm} \]
\[ V = 960 \, \text{cm}^3 \]

### Step 3: Calculate the surface area of the cuboid
The formula for the surface area (SA) of a cuboid is:
\[ SA = 2(lb + bh + lh) \]

Calculating each term:
1. \( lb = 12 \, \text{cm} \times 10 \, \text{cm} = 120 \, \text{cm}^2 \)
2. \( bh = 10 \, \text{cm} \times 8 \, \text{cm} = 80 \, \text{cm}^2 \)
3. \( lh = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2 \)

Now, add these areas together:
\[ lb + bh + lh = 120 \, \text{cm}^2 + 80 \, \text{cm}^2 + 96 \, \text{cm}^2 = 296 \, \text{cm}^2 \]

Now, substitute this back into the surface area formula:
\[ SA = 2 \times 296 \, \text{cm}^2 = 592 \, \text{cm}^2 \]

### Final Answers:
- Volume of the cuboid = \( 960 \, \text{cm}^3 \)
- Surface Area of the cuboid = \( 592 \, \text{cm}^2 \)

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