Diameters of circles

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

Correct answer:

p =  16 %

Step-by-step explanation:

$$\begin{gathered} D_1=120\text{mm} \\ {D}_2=300\text{mm} \\ {r}_1=D_1/2=120/2=60\text{mm} \\ {r}_2=D_2/2=300/2=150\text{mm} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 60^2\doteq 11309.7336{\text{mm}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 150^2\doteq 70685.8347{\text{mm}}^2 \\ p=S_1/S_2\cdot 100=11309.7336/70685.8347\cdot 100=16\% \end{gathered}$$

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