Shortcut Trick
6 individual cubes have a total of 6 × 6 = 36 faces.
Joining them end-to-end forms 5 joints between the cubes.
Each joint hides 2 faces, leaving 36 − (5 × 2) = 26 visible faces.
Area of each square face = a2 = 22 = 4 cm2.
Total surface area = 26 × 4 = 104 cm2.
∴ The correct answer is 104 cm2.
Alternate Method
Given:
Number of cubes = 6
Edge of each cube (a) = 2 cm
Formula Used:
Total Surface Area of a Cuboid = 2(lb + bh + hl)
Calculations:
When 6 uniform cubes are joined end to end, a cuboid is formed where the length increases but breadth and height remain unchanged.
⇒ Length of the resulting cuboid (l) = 6 × 2 = 12 cm
⇒ Breadth of the resulting cuboid (b) = 2 cm
⇒ Height of the resulting cuboid (h) = 2 cm
⇒ Total Surface Area = 2 × (l × b + b × h + h × l)
⇒ Total Surface Area = 2 × (12 × 2 + 2 × 2 + 2 × 12)
⇒ Total Surface Area = 2 × (24 + 4 + 24)
⇒ Total Surface Area = 2 × 52 = 104 cm2
∴ The correct answer is 104 cm2.
Additional Information
Total Surface Area of a Cube
The total surface area of a single cube of edge length 'a' is given by 6a2, as it is composed of 6 identical square faces.
Joining 'n' Cubes
When 'n' cubes of side 'a' are joined end-to-end, the resulting shape is a cuboid with length 'n × a', while the breadth and height remain 'a'.
Lateral Surface Area
The lateral (or curved) surface area of a cuboid excludes the top and bottom faces. It is given by the formula LSA = 2h(l + b).