Question #14da6

1 Answer
May 24, 2017

Answer:

#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#