Three faces of a cuboid that meet at one corner have areas 48 cm², 60 cm² and 80 cm². What is the volume of the cuboid?

Explanation

1. 01

   If the edges are l, b and $h$, the face areas are lb, bh and hl.

2. 02

   Their product is (lbh)², so $(lbh)^2 = 48 \times 60 \times 80 = 2{,}30{,}400$.

3. 03

   Volume = $\sqrt{2{,}30{,}400} = 480$ cm³. (The edges are 6, 8 and 10 cm.)