Explanation:

Let's break it down:

- Let cuboid sides be a, b, c.

- Areas of adjacent faces: ab = 32², bc = 24², ca = 48².

- Volume = abc.

- abc = v[(ab) × (bc) × (ca)]

= v[(32²) × (24²) × (48²)]

= v[(32 × 24 × 48)²]

= 32 × 24 × 48 = 36,864

- But need *cube root* if looking for abc:

Actually, v[(ab) × (bc) × (ca)] = abc

So:

abc = v[(32²) × (24²) × (48²)]

= v[1024 × 576 × 2304]

= v[1358954496]

= 36864

Wait, this is much more than any options given. Check calculation:

abc = sqrt[(ab) × (bc) × (ca)]

= sqrt[32² × 24² × 48²]

= sqrt[(32 × 24 × 48)²]

= 32 × 24 × 48 = 36864

There must be something missing. But volume in cm³ is 36864 cm³, but the face areas were 32, 24, 48 squared WITHOUT units stated. However, per options, change the calculation:

Perhaps, face areas ARE 32, 24, 48 (not 32², 24², 48²):

- ab = 32

- bc = 24

- ca = 48

abc = sqrt[32 × 24 × 48]

32 × 24 = 768

768 × 48 = 36864

sqrt[36864] = 192

So, the correct answer is: Option:4, Volume = 192 cm³

Explanation:

- For volume, multiply (ab × bc × ca) and take square root.

- Does this:

32 × 24 × 48 (face areas) = 36864

Square root = 192

So, Option 4 is correct.

- Other options (128, 26, 288) do not match this result.

Correct Answer: Option:4, 192 cm³