Flowerbed

We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.

Result

r1 =  1.5 m

Solution:

r2=r1+3 S2=9 S1 πr22=9 πr12 r22=9 r12 r2=3 r1   r2=r1+3 r2=3 r1  r1r2=3 3r1r2=0  r1=32=1.5 =32=1.5  m  r2=92=4.5 r_{ 2 } = r_{ 1 } + 3 \ \\ S_{ 2 } = 9 \ S_{ 1 } \ \\ \pi r_{ 2 }^2 = 9 \ \pi r_{ 1 }^2 \ \\ r_{ 2 }^2 = 9 \ r_{ 1 }^2 \ \\ r_{ 2 } = 3 \ r_{ 1 } \ \\ \ \\ \ \\ r_{ 2 } = r_{ 1 } + 3 \ \\ r_{ 2 } = 3 \cdot \ r_{ 1 } \ \\ \ \\ r_{ 1 }-r_{ 2 } = -3 \ \\ 3r_{ 1 }-r_{ 2 } = 0 \ \\ \ \\ r_{ 1 } = \dfrac{ 3 }{ 2 } = 1.5 \ \\ = \dfrac{ 3 }{ 2 } = 1.5 \ \text{ m } \ \\ r_{ 2 } = \dfrac{ 9 }{ 2 } = 4.5 \ \\



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