Question

If two cubes each of volume 8 cm\(^3\) are joined end-to-end, then the surface area of the resulting cuboid will be:

• A. 48 cm\(^2\)
• B. 44 cm\(^2\)
• C. 40 cm\(^2\)
• D. 30 cm\(^2\)

Hint:

When solids are joined, always subtract the area of the common face(s) to avoid double counting.

Answer 1

The Correct Option is B

Step 1: Find the side of one cube.
Volume of cube \( = a^3 = 8 \Rightarrow a = 2 \text{ cm} \).

Step 2: When two cubes are joined end-to-end.
The cuboid formed will have dimensions: Length = \( 2a = 4 \text{ cm} \), Breadth = \( a = 2 \text{ cm} \), Height = \( a = 2 \text{ cm} \).

Step 3: Use surface area formula.
\[ \text{Surface Area} = 2(lb + bh + hl) \] \[ = 2(4\times2 + 2\times2 + 2\times4) = 2(8 + 4 + 8) = 2(20) = 40 \text{ cm}^2 \] Wait — but when two cubes are joined, one face (area = \(2\times2=4\)) of each cube becomes internal and is not exposed. Hence, total area = \( 48 - 4 = 44 \text{ cm}^2 \).

Step 4: Conclusion.
Therefore, the surface area of the cuboid is \( \boxed{44\text{ cm}^2} \).