CUET UG 2025 — General Test Geometry

The three adjacent faces of a cuboid have areas that represent the products of different pairs of dimensions.

For a cuboid with length $l$l, width $w$w, and height $h$h:

$$l \times w = 96$$l×w=96

$$w \times h = 48$$w×h=48

$$l \times h = 72$$l×h=72

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Multiplying all three equations:

$$(l \times w) \times (w \times h) \times (l \times h) = 96 \times 48 \times 72$$(l×w)×(w×h)×(l×h)=96×48×72

$$l^2 \times w^2 \times h^2 = 96 \times 48 \times 72$$l2×w2×h2=96×48×72

$$(l \times w \times h)^2 = 96 \times 48 \times 72$$(l×w×h)2=96×48×72

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Calculating the right side:

$$96 \times 48 = 4608$$96×48=4608

$$4608 \times 72 = 331776$$4608×72=331776

Therefore:

$$(l \times w \times h)^2 = 331776$$(l×w×h)2=331776

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Taking the square root of both sides:

$$l \times w \times h = \sqrt{331776}$$l×w×h=331776​

$$l \times w \times h = 576$$l×w×h=576

Since volume $= l \times w \times h$=l×w×h, the volume of the box is $576$576 cm³.