A jeweler markets novelty "gold-marble" paperweights. Each paperweight consists of a small spherical gold core (density 19.3×103kgm−3) surrounded by a spherical shell of white marble (density 2.70×103kgm−3). The outer radius of every paperweight is fixed at 2.50cm, but different models contain different amounts of gold.
Answer the following questions about a particular model whose total mass is measured to be 230g.
(a) Calculate the overall density of this paperweight in kgm−3. Show all work, including any required unit conversions.
(b) Determine the radius of the gold core that yields the measured total mass. Express your answer in centimeters.
(c) If the paperweight is gently lowered into a large tank of water (density 1.0×103kgm−3), predict whether it will sink or float. Justify your answer using your result from part (a).