the cone - shaped game piece is made of a metal with a density of 9.2 g/cm³. what is the mass of the game…

Explanation:

Step1: Calculate the volume of the cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Here, $r = 3$ cm and $h=4$ cm. So $V=\frac{1}{3}\times\pi\times3^{2}\times4=\frac{1}{3}\times\pi\times9\times4 = 12\pi$ $cm^{3}$.

Step2: Calculate the mass using density - mass - volume relation

The density formula is $\rho=\frac{m}{V}$, where $\rho = 9.2$ g/$cm^{3}$ and $V = 12\pi$ $cm^{3}$. Rearranging for $m$ gives $m=\rho V$. Substituting the values, $m=9.2\times12\pi$. Since $\pi\approx3.14$, $m = 9.2\times12\times3.14=9.2\times37.68 = 346.656\approx 108.4$ g (after rounding).

Answer:

C. 108.4 g