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?

Result

p =  16 %

Solution:

D1=120 mm D2=300 mm r1=D1/2=120/2=60 mm r2=D2/2=300/2=150 mm S1=π⋅ r12=3.1416⋅ 602≐11309.7336 mm2 S2=π⋅ r22=3.1416⋅ 1502≐70685.8347 mm2 p=S1/S2⋅ 100=11309.7336/70685.8347⋅ 100=16=16%D_{ 1 } = 120 \ mm \ \\ D_{ 2 } = 300 \ mm \ \\ r_{ 1 } = D_{ 1 }/2 = 120/2 = 60 \ mm \ \\ r_{ 2 } = D_{ 2 }/2 = 300/2 = 150 \ mm \ \\ S_{ 1 } = \pi \cdot \ r_{ 1 }^2 = 3.1416 \cdot \ 60^2 \doteq 11309.7336 \ mm^2 \ \\ S_{ 2 } = \pi \cdot \ r_{ 2 }^2 = 3.1416 \cdot \ 150^2 \doteq 70685.8347 \ mm^2 \ \\ p = S_{ 1 }/S_{ 2 } \cdot \ 100 = 11309.7336/70685.8347 \cdot \ 100 = 16 = 16 \%

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