Cuboid walls

If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.

Result

V =  60 cm³

Solution:

$ab = 8 \ \\ bc = 18 \ \\ ca = 25 \ \\ \ \\ V = abc \ \\ ab \cdot \ bc \cdot \ ca = a^2 \cdot \ b^2 \cdot \ c^2 = (abc)^2 = V^2 \ \\ \ \\ V = \sqrt{ 8 \cdot \ 18 \cdot \ 25 } = 60 = 60 \ cm^3$

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