Final answer:
To find the surface area of the resulting cuboid formed by joining two cubes of volume 64 cm³, calculate the dimensions of the cuboid and use the surface area formula.
Step-by-step explanation:
To find the surface area of the resulting cuboid, we need to find the dimensions of the cuboid formed by joining the two cubes. Since each cube has a volume of 64 cm³, the side length of each cube can be found by taking the cube root of the volume: ∛64 = 4 cm. When the two cubes are joined end to end, the resulting cuboid will have dimensions of 8 cm (length), 4 cm (width), and 4 cm (height).
The surface area of a cuboid is given by the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the cuboid. Substituting the values l = 8 cm, w = 4 cm, and h = 4 cm into the formula, we get: SA = 2(8)(4) + 2(8)(4) + 2(4)(4) = 160 cm².
Therefore, the surface area of the resulting cuboid is 160 cm².