Prescribed 4579

The racing ball for men has a prescribed weight of 7250g. It is made of iron. How does its diameter change if we make it from lead? The density of iron is 7.8 g / cm cubic, and the density of lead is 11.3 t / m cubic.

Correct answer:

D₁ =  12.1083 cm
D₂ =  10.7009 cm

Step-by-step explanation:

$$\begin{gathered} m=7250\text{g} \\ {\rho }_1=7.8{\text{g/cm}}^3 \\ {\rho }_2=11.3{\text{g/cm}}^3 \\ {V}_1=m/{\rho }_1=7250/7.8=\frac{36250}{39}\doteq 929.4872{\text{cm}}^3 \\ V=4/3\pi r^3=4/3\pi (D/2{)}^3=\pi /6D^3 \\ {D}_1=\sqrt[3]{6\cdot V_1/\pi }=\sqrt[3]{6\cdot 929.4872/3.1416}=12.1083\text{cm} \end{gathered}$$

$$\begin{gathered} V_2=m/{\rho }_2=7250/11.3\doteq 641.5929{\text{cm}}^3 \\ {D}_2=\sqrt[3]{6\cdot V_2/\pi }=\sqrt[3]{6\cdot 641.5929/3.1416}=10.7009\text{cm} \end{gathered}$$

Try another example