Question

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 1

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)

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∴lbh=2×2×3×5=60cubic cm

∴ Volume of the cuboid=lbh=60cu

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