Answer
The mass of the gold cylinder is 19,251.75 g and the mass of the sand cylinder is 2,992.5 g.
Work Step by Step
First, you calculate the volume of the cylinder using the volume equation ( $πr^{2}h$ ). You plug the radius of the cylinder (3.8 cm) into the equation for r. And then plug in the height of the cylinder (22 cm) in for h. You simplify it and get $\approx 997.5 cm^{3}$.
Then to get the mass of the gold cylinder, you set up a proportion by setting the density of gold
($19.3g/1 cm^{3}$) equal to $x grams/997.5 cm^{3}$ (the weight of the gold cylinder over the volume of the cylinder). Simplify and you get 19,251.75 g.
Do the same thing to get the mass of the sand cylinder. Set the density of sand
($3.00g/1 cm^{3}$) equal to $x grams/997.5 cm^{3}$ (the weight of the sand cylinder over the volume of the cylinder). Simplify and you get 2,992.5 g.
