Question

Question #14da6

Answer 1

`0.81"g"/"cm"^3`

Explanation:

The volume of a cylinder is represented by the equation

`V = pir^2h`

Which, if you might notice, is simply the equation for the area of a circle, `pir^2`, multiplied by the height, `h`.

The diameter is equal to `2r`, so `r = 1/2(0.5"m") = 0.25"m"`

The volume of the cylinder is thus

`V = pi(0.25m)^2(0.75m) = 0.15 "m"^3`

The equation for density is

`rho = m/V`

Density is equal to the mass of the substance per unit volume.

Density is often expressed in units of `"g"/"cm"^3`, so let's convert our units to these:

`0.15cancel("m"^3)((100^3"cm"^3)/(1cancel("m"^3))) = 1.5 xx 10^5 "cm"^3`

`122cancel("kg")((10^3"g")/(1cancel("kg"))) = 1.22 xx 10^5 "g"`

So our density is, in `"g"/"cm"^3`,

`rho = (1.22 xx 10^5 "g")/(1.5 xx 10^5 "cm"^3) = color(red)(0.81"g"/"cm"^3`