Discussion
If the areas of the three adjacent faces of a cuboidal box are 120cm2, 72cm2 and 60cm2 respectively, find the volume of the box.
Answer: B
With faces \( P = lb \), \( Q = bh \), \( R = hl \), the product of all three is the square of the volume:
\[ PQR = (lbh)^{2} \quad\Longrightarrow\quad V = \sqrt{PQR} \]
\[ V = \sqrt{120 \times 72 \times 60} = \sqrt{518400} = 720 \text{ cm}^{3} \]
Forgetting the square root leaves 518,400; the dimensions themselves work out to 10, 12 and 6 cm, which do reproduce all three given face areas.
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