Geometry

Solids

Medium

The areas of three adjacent faces of a cuboidal box are 96 cm², 48 cm² and 72 cm², respectively. The volume of the box is

720 cm³

576 cm³

288 cm³

420 cm³

✅ Correct Option: 2

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

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

$l \times w = 96$

$w \times h = 48$

$l \times h = 72$

Multiplying all three equations:

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

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

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

Calculating the right side:

$96 \times 48 = 4608$

$4608 \times 72 = 331776$

Therefore:

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

Taking the square root of both sides:

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

$l \times w \times h = 576$

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

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Solution

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