Diameters of circles

How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?

Correct answer:

p =  16 %

Step-by-step explanation:

$$\begin{gathered} D_1=120\text{ mm } \\ {D}_2=300\text{ mm } \\ {r}_1=D_1\mathrm{/}2=120\mathrm{/}2=60\text{ mm } \\ {r}_2=D_2\mathrm{/}2=300\mathrm{/}2=150\text{ mm } \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 60^2\doteq 11309.7336{\text{mm}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 150^2\doteq 70685.8347{\text{mm}}^2 \\ p=S_1\mathrm{/}{S}_2\cdot 100=11309.7336\mathrm{/}70685.8347\cdot 100=16\mathrm{\%} \end{gathered}$$

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