Gold ring

A gold ring with a width of 1 cm is made by drilling a sphere with a radius of 1 cm through its center. A gold bracelet with a width of 1 cm is made by drilling a sphere with a radius of 4 cm through its center. Which piece of jewelry will be worth more if we only consider the amount of precious metal?

Correct answer:

x =  2

Step-by-step explanation:

$$\begin{gathered} D_1=1\text{cm} \\ {r}_1=1\text{cm} \\ {D}_2=1\text{cm} \\ {r}_2=4\text{cm} \\ m=\rho V \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r_1^3=\frac{4}{3}\cdot 3.1416\cdot 1^3\doteq 4.1888{\text{cm}}^3 \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r_2^3=\frac{4}{3}\cdot 3.1416\cdot 4^3\doteq 268.0826{\text{cm}}^3 \\ {V}_2-V_3>V_1-V_4 \\ {V}_2>V_1 \\ x=2 \end{gathered}$$

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