Find the volume and the total surface area of a cuboid ,whose :
length = 15 cm , breadth = 10 cm and height = 8 cm

Answer

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

### Step 1: Identify the dimensions of the cuboid
- Length (l) = 15 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:
\[ V = 15 \, \text{cm} \times 10 \, \text{cm} \times 8 \, \text{cm} \]

Calculating:
\[ V = 15 \times 10 = 150 \, \text{cm}^2 \]
\[ V = 150 \times 8 = 1200 \, \text{cm}^3 \]

So, the volume of the cuboid is **1200 cm³**.

### Step 3: Calculate the total surface area of the cuboid
The formula for the total surface area (SA) of a cuboid is:
\[ SA = 2(l \times b + b \times h + h \times l) \]

Substituting the values:
\[ SA = 2(15 \, \text{cm} \times 10 \, \text{cm} + 10 \, \text{cm} \times 8 \, \text{cm} + 8 \, \text{cm} \times 15 \, \text{cm}) \]

Calculating each term:
1. \( l \times b = 15 \times 10 = 150 \, \text{cm}^2 \)
2. \( b \times h = 10 \times 8 = 80 \, \text{cm}^2 \)
3. \( h \times l = 8 \times 15 = 120 \, \text{cm}^2 \)

Now, add these areas:
\[ 150 + 80 + 120 = 350 \, \text{cm}^2 \]

Now, multiply by 2 for the total surface area:
\[ SA = 2 \times 350 = 700 \, \text{cm}^2 \]

So, the total surface area of the cuboid is **700 cm²**.

### Final Answers:
- Volume = **1200 cm³**
- Total Surface Area = **700 cm²**