We are asked to determine the density of a gulf ball given its mass and volume. To do that, we will use the formula for density:
[tex]D=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]To determine the volume we will use the fact that the gulf ball can be approximated to a sphere and the volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where:
[tex]r=\text{ radius}[/tex]We are given the diameter. We know that the diameter is twice the radius, therefore:
[tex]r=\frac{D}{2}[/tex]Substituting the value of the diameter we get:
[tex]r=\frac{4.287\operatorname{cm}}{2}[/tex]Solving the operations:
[tex]r=2.144\operatorname{cm}[/tex]Now, we substitute the value of the radius in the formula of the volume:
[tex]V=\frac{4}{3}\pi(2.144\operatorname{cm})^3[/tex]Solving the operation we get:
[tex]V=41.282\operatorname{cm}^3[/tex]Now, we substitute the value of the volume and the mass in the formula for density:
[tex]D=\frac{45.87g}{41.282\operatorname{cm}^3}[/tex]Solving the operation:
[tex]D=1.11\frac{g}{\operatorname{cm}^3}[/tex]Therefore, the density of the ball is 1.11 g/cm^3.
