2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

We will find the length of the edge of each cube by using the formula for the volume of a cube = a³, where the length of the edge is 'a'.

As the cubes are joined end to end, they will appear as follows:

Using the formula for the surface of cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively.

Let the length of the edge of each cube be 'a'.

Therefore, the volume of the cube = a³

The volume of the cube, a³ = 64 cm³

a³ = 64 cm³

a = ∛(64 cm³)

a = 4 cm

Therefore,

Length of the resulting cuboid, l = a = 4 cm

Breadth of the resulting cuboid, b = a = 4 cm

Height of the resulting cuboid, h = 2a = 2 × 4 cm = 8 cm

Surface area of the resulting cuboid = 2 (lb + bh + lh)

= 2(4 cm × 4 cm + 4 cm × 8 cm + 4 cm × 8 cm)

= 2(16 cm² + 32 cm² + 32 cm²)

= 2 × 80 cm²

= 160 cm²

Thus, the surface area of the resulting cuboid is 160 cm².