Question

1)   We find a fairly heavy gold color spherical metal ball and decide to find out if it is pure gold or not by using the density formula, 𝑑 =mass/density. The density of pure gold is found to be 19.32 𝑔/𝑐m³. (a)   So, we carefully measure the radius of the metal ball 𝑟 ± ∆𝑟 = 1.50 ± 0.05 𝑐m. Calculate the volume of the ball, 𝑉sphere = 4/3 𝜋𝑟³, and its uncertainty, 𝑉 ± ∆𝑉. (a)  Then, using the density formula, calculate the value of the mass and its uncertainty, 𝑚 ± ∆𝑚, to show what should be the measured value of the mass for the metal ball to be pure gold.  

Answer 1

$$m=\frac{4}{3}\pi(1.5)^3(19.32)=273.13\ g\\\Delta m=3(273.13)\frac{0.05}{1.5}=27\ g$$