The front, side, and bottom faces of a rectangular solid have areas of 24 square centimeters, 8 square centimeters, and 3 square centimeters, respectively. What is the volume of the solid, in cubic centimeters?

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Answer 1 · 2018-07-18T14:01:31

$color(magenta)( V = l b h = 24 cm^3$

Let l, b, h be the three sides of the cuboid.

Given $l * b = 24 cm^2$

$b * h = 8 cm^2$

$h * l = 3 cm^2$

$l b * b h * h l = (lbh)^2 = 24 * 8 * 3 = 576$

$l b h = sqrt 576 = 24$

Volume of cuboid $V = l * b * h$

$:. color(magenta)( V = l b h = 24 cm^3$