Approximately 28431

On the 200th anniversary of the birth of Ľudovít Štúr, the National Bank of Slovakia issued a commemorative two-euro coin in 2015, the diameter of which is 25.75 mm. The nickel-brass center is approximately 18 millimeters in diameter; the rest of the coin is medi-nickel. Around mm², are the areas of these parts of the coin different?

Correct answer:

x =  11.8301 mm²

Step-by-step explanation:

$$\begin{gathered} D=25.75\text{mm} \\ {D}_1=18\text{mm} \\ {S}_1=\pi \cdot (D_1/2{)}^2=3.1416\cdot (18/2{)}^2\doteq 254.469{\text{mm}}^2 \\ {S}_2=\pi \cdot (D/2{)}^2-S_1=3.1416\cdot (25.75/2{)}^2-254.469\doteq 266.2991{\text{mm}}^2 \\ x=S_2-S_1=266.2991-254.469=11.8301{\text{mm}}^2 \end{gathered}$$

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