I keep getting the answer wrong!

Question

A cylindrical glass tube 20.0 cm in length is filled with acetone . The mass of the acetone to fill the tube is found to be 18.73g. Calculate the inner diameter of the tube in cm . The density of acetone is 0.784g/mL

Answer 1

Starting with the density equation: mass / volume = density.

we know the mass of the acetone to be 18.73 g. The density is known to be 0.784 g/mL. the height of the cylinder is 20.0cm

our unknown is the volume of acetone. This is equivalent to the volume of the cylindrical tube since the acetone completely fills the tube.

the volume of a cylinder is given by pi*r²*h where r = radius of the cylinder and h = height of the cylinder.

plugging this into the density equation we get (mass / pi*r²*h) = density.

rearranging the equation to solve for r gives r = sqrt[mass/(density*pi*h)]

since diameter is 2 * r we can say that the diameter equals 2*sqrt[mass/(density*pi*h)] = 2*sqrt(18.73g/(0.784g/mL*pi*20cm)) = 1.23 cm