For a solid and pure metal sphere (ball) with radius of 4.104 cm. If the mass of the metal sphere was measured as 15.3 g, what is the density of the metal?

We have given the radius and the mass of the metal sphere. The formula for calculating a sphere's density is mass over volume ($\frac{mass}{volute}$) . To calculate the volume, we can use this formula: $\frac 43 \pi r^2$.

If we put the given radius in the volume formula,

V = $\frac 43 \times \pi \times 4.104^3$ = 289.5 cm³

Note: If the question is related to significant figures (SF), leave the answer just up to the fourth significant figure, i.e., 289.5. To calculate the SF, we should revise our calculation procedure. 4/3 and Pi are omitted since they are constants, but 4.104 is not omitted because it is the value of the radius and it has cm as a unit. 4.104 has 4 SFs, so our final answer must have 4 SFs.

We have got the volume. Let's calculate the density,

D = $\frac{mass}{volute}$ = $\frac{15.3}{289.5}$ = 0.0528 g/cm³

Note: We limit our answer up to 0.0528, i.e., 3 significant figures (SFs). Because in the calculation process, the numerator has 3 SFs and the denomenator has 4 SFs.