Four cubes each of volume 216 cubic cm are joined end to end to form a new solid. The surface area of the new solid is:

The correct option is 672 sq cm.

Step 1: Find the side length of a single cube.

Let a be the side length (edge) of each cube.

The volume of a cube is given by the formula:

$a^3=\text{Volume}$

Given that the volume of each cube is 216 cm³:

$a^3=216$

$a=\sqrt[3]{216}$

$a=6\text{cm}$

Step 2: Determine the dimensions of the new solid (cuboid).

When four identical cubes are joined end to end in a line, they form a cuboid.

The dimensions of the resulting cuboid will be:

Length (l) = 4 × a = 4 × 6 = 24 cm

Breadth (b) = a = 6 cm

Height (h) = a = 6 cm

Step 3: Calculate the total surface area of the cuboid.

The formula for the total surface area of a cuboid is:

$\text{Surface Area}=2(lb+bh+hl)$

Substituting the values of l, b, and h:

$\text{Surface Area}=2(24\times 6+6\times 6+6\times 24)$

$\text{Surface Area}=2(144+36+144)$

$\text{Surface Area}=2\left(324\right)$

$\text{Surface Area}=672\text{sq cm}$

Therefore, the surface area of the new solid is 672 sq cm.