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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