Two adjacent faces of a cuboid box, having all its sides with integral values (in cm), have an area of 32 cm² and 40 cm² respectively. What is the ratio of the maximum possible volume
of the cuboid to the minimum possible volume?
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Answer:
Given: A1=lb=8sq.cm
A2=bh=18sq.cm
A3=lh=25sq.cm
⇒lb×bh×lh=8×18×25
⇒(lbh)2=2×2×2×3×3×2×5×5
⇒lbh=(2×2×2×3×3×2×5×5)
∴lbh=2×2×3×5=60cubic cm
∴ Volume of the cuboid=lbh=60cu
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