# A block of wood 3.0 cm on each side has a mass of 27 g. What is the density of this block?

Jul 8, 2018

The density is $1 \frac{g}{c {m}^{3}}$. See explanation.

#### Explanation:

The density of an object is calculated as the ratio of its mass and volume:

## $d = \frac{m}{V}$

Here the volume is not given, but can be calculated using the given dimension:

## $V = {a}^{3}$

Now we can calculate the density using the given data:

## $V = \frac{m}{{a}^{3}}$

Now we can put the values:

$V = \frac{27}{{3}^{3}} = \frac{27}{27} = 1$

Answer: The density is $d = 1 \frac{g}{c {m}^{3}}$.

Jul 8, 2018

${\rho}_{\text{block}} = 1 \cdot g \cdot c {m}^{-} 3$

#### Explanation:

${\rho}_{\text{density"="Mass of stuff"/"volume of stuff}}$.

Here we got a cube whose mass is $27 \cdot g$...and we know how to calculate the volume of a cube, i.e. it is simpy the CUBE of an edge length...

And so ${\rho}_{\text{block"=underbrace(27*g)_"mass of the block"/underbrace(3*cmxx3*cmxx3*cm)_"volume of the block}} = \frac{27 \cdot g}{27 \cdot c {m}^{3}} = 1 \cdot g \cdot c {m}^{-} 3$.

Would the block of wood float on water?