# 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 result:

p =  16 %

#### Solution:

$D_{1}=120 \ \text{mm} \ \\ D_{2}=300 \ \text{mm} \ \\ r_{1}=D_{1}/2=120/2=60 \ \text{mm} \ \\ r_{2}=D_{2}/2=300/2=150 \ \text{mm} \ \\ S_{1}=\pi \cdot \ r_{1}^2=3.1416 \cdot \ 60^2 \doteq 11309.7336 \ \text{mm}^2 \ \\ S_{2}=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 150^2 \doteq 70685.8347 \ \text{mm}^2 \ \\ p=S_{1}/S_{2} \cdot \ 100=11309.7336/70685.8347 \cdot \ 100=16 \%$

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