Three cubes , each of edge 8 cm , are joined as shown alongside . Find the total surface area and the volume of the cuboid.

Answer

To find the total surface area and volume of the cuboid formed by joining three cubes, each with an edge length of 8 cm, we can follow these steps:

### Step 1: Calculate the Volume of the Cuboid
The volume of a cuboid can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

#### Calculation:
- Since three cubes are joined together, the total length of the cuboid will be:
\[ \text{Length} = 8 \, \text{cm} + 8 \, \text{cm} + 8 \, \text{cm} = 24 \, \text{cm} \]
- The breadth and height of the cuboid will be the same as the edge of the cube:
\[ \text{Breadth} = 8 \, \text{cm}, \quad \text{Height} = 8 \, \text{cm} \]

Now substituting the values into the volume formula:
\[ \text{Volume} = 24 \, \text{cm} \times 8 \, \text{cm} \times 8 \, \text{cm} = 24 \times 64 \, \text{cm}^3 \]

Calculating \(24 \times 64\):
\[ 24 \times 64 = 1536 \, \text{cm}^3 \]

### Step 2: Calculate the Total Surface Area of the Cuboid
The total surface area of a cuboid can be calculated using the formula:
\[ \text{Total Surface Area} = 2 \times (\text{Length} \times \text{Breadth} + \text{Breadth} \times \text{Height} + \text{Height} \times \text{Length}) \]

#### Calculation:
Substituting the values we have:
\[ \text{Total Surface Area} = 2 \times (24 \, \text{cm} \times 8 \, \text{cm} + 8 \, \text{cm} \times 8 \, \text{cm} + 8 \, \text{cm} \times 24 \, \text{cm}) \]

Calculating each term:
1. \(24 \times 8 = 192 \, \text{cm}^2\)
2. \(8 \times 8 = 64 \, \text{cm}^2\)
3. \(8 \times 24 = 192 \, \text{cm}^2\)

Now adding these:
\[ 192 + 64 + 192 = 448 \, \text{cm}^2 \]

Now substituting back into the surface area formula:
\[ \text{Total Surface Area} = 2 \times 448 \, \text{cm}^2 = 896 \, \text{cm}^2 \]

### Final Answers:
- **Volume of the cuboid**: \(1536 \, \text{cm}^3\)
- **Total Surface Area of the cuboid**: \(896 \, \text{cm}^2\)

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