Question

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

Answer 1

The density is `1g/(cm^3)`. See explanation.

Explanation:

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

`d=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=m/(a^3)`

Now we can put the values:

`V=27/(3^3)=27/27=1`

Answer: The density is `d=1g/(cm^3)`.

Answer 2

`rho_"block"=1*g*cm^-3`

Explanation:

`rho_"density"="Mass of stuff"/"volume of stuff"`.

Here we got a cube whose mass is `27*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_"block"=underbrace(27*g)_"mass of the block"/underbrace(3*cmxx3*cmxx3*cm)_"volume of the block"=(27*g)/(27*cm^3)=1*g*cm^-3`.

Would the block of wood float on water?