# A piece of metal that measures 33.0 cm by 46.0 cm by 48.0 cm has a mass of 800.0 grams. What is the density of the metal? Would the piece of metal float in water?

Apr 1, 2018

${\rho}_{\text{metal}} = 0.07 \cdot g \cdot c {m}^{-} 3$

#### Explanation:

By definition, ${\rho}_{\text{metal"="mass of metal"/"volume of metal}}$

$= \frac{800 \cdot g}{33.0 \cdot c m \times 46.0 \cdot c m \times 48.0 \cdot c m} = 0.0659 \cdot g \cdot c {m}^{-} 3$

And this is an IMPROBABLY undense metal. The LEAST dense metal, lithium, is approx. $0.5 \cdot g \cdot c {m}^{-} 3$...(at any rate this metal reacts with water)...the question is unreasonable and should not have been proposed.

Given the density, the metal would float in water (if it didn't react with it!).