If 2 cubes are connected on their bases, the Total Surface Area(TSA) of the new object formed is -

Options

A. Less than the sum of TSA of two cubes
B. More than the sum of TSA of two cubes
C. Equal to the sum of TSA of two cubes
D. None of these

Answer

To find the Total Surface Area (TSA) of two cubes connected at their bases, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Side Length of the Cube:**
Let the side length of each cube be \( A \).

2. **Calculate the Total Surface Area of One Cube:**
The formula for the total surface area (TSA) of a cube is:
\[ \text{TSA of one cube} = 6A^2 \]
Therefore, for two cubes:
\[ \text{TSA of two cubes} = 2 \times 6A^2 = 12A^2 \]

3. **Understand the New Shape Formed:**
When two cubes are connected at their bases, they form a cuboid. The dimensions of this new cuboid are:
- Length \( L = 2A \) (since the two cubes are placed side by side)
- Width \( B = A \)
- Height \( H = A \)

4. **Calculate the Total Surface Area of the Cuboid:**
The formula for the total surface area of a cuboid is:
\[ \text{TSA of cuboid} = 2(LB + BH + LH) \]
Substituting the dimensions:
\[ \text{TSA of cuboid} = 2(2A \cdot A + A \cdot A + 2A \cdot A) \]
Simplifying this:
\[ = 2(2A^2 + A^2 + 2A^2) = 2(5A^2) = 10A^2 \]

5. **Compare the Total Surface Areas:**
Now we compare the TSA of the two cubes and the TSA of the cuboid:
- TSA of two cubes = \( 12A^2 \)
- TSA of the cuboid = \( 10A^2 \)

Since \( 10A^2 < 12A^2 \), we conclude that the TSA of the new object (cuboid) is less than the TSA of the two separate cubes.

### Final Answer:
The Total Surface Area (TSA) of the new object formed by connecting two cubes at their bases is \( 10A^2 \), which is less than the TSA of the two individual cubes.

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