Find the volume and the surface area of a cuboid with dimensions:
length = 8 cm , breadth = 2.5 cm , heigth = 2cm

Answer

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

### Given:
- Length (l) = 8 cm
- Breadth (b) = 2.5 cm
- Height (h) = 2 cm

### Step 1: Calculate the Volume of the Cuboid
The formula for the volume (V) of a cuboid is given by:
\[ V = l \times b \times h \]

Substituting the values:
\[ V = 8 \, \text{cm} \times 2.5 \, \text{cm} \times 2 \, \text{cm} \]

Calculating:
1. First, convert 2.5 cm to a fraction for easier calculation:
\[ 2.5 \, \text{cm} = \frac{5}{2} \, \text{cm} \]

2. Now substitute:
\[ V = 8 \times \frac{5}{2} \times 2 \]

3. Simplifying:
- The 2 in the numerator and denominator cancels out:
\[ V = 8 \times 5 = 40 \, \text{cm}^3 \]

### Step 2: Calculate the Surface Area of the Cuboid
The formula for the surface area (SA) of a cuboid is given by:
\[ SA = 2(lb + bh + hl) \]

Substituting the values:
\[ SA = 2 \left( (8 \, \text{cm} \times 2.5 \, \text{cm}) + (2.5 \, \text{cm} \times 2 \, \text{cm}) + (2 \, \text{cm} \times 8 \, \text{cm}) \right) \]

Calculating each term:
1. Calculate \( lb \):
\[ lb = 8 \times 2.5 = 20 \, \text{cm}^2 \]

2. Calculate \( bh \):
\[ bh = 2.5 \times 2 = 5 \, \text{cm}^2 \]

3. Calculate \( hl \):
\[ hl = 2 \times 8 = 16 \, \text{cm}^2 \]

Now substitute back into the surface area formula:
\[ SA = 2 \left( 20 + 5 + 16 \right) \]

Calculating the sum:
\[ SA = 2 \times 41 = 82 \, \text{cm}^2 \]

### Final Answers:
- Volume = 40 cm³
- Surface Area = 82 cm²

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