Four circles

1) Calculate the circle radius if its area is 400 cm square
2) Calculate the radius of the circle whose circumference is 400 cm.
3) Calculate circle circumference if its area is 400 cm square
4) Calculate the circle's area if the perimeter is 400 cm.

Correct answer:

r₁ =  11.2838 cm
r₂ =  63.662 cm
o₁ =  70.8982 cm
S₂ =  12732.3954 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=400{\text{cm}}^2 \\ {S}_1=\pi r_1^2 \\ {r}_1=\sqrt{S_1/\pi }=\sqrt{400/3.1416}=11.2838\text{cm} \end{gathered}$$

$$\begin{gathered} o_2=400\text{cm} \\ {o}_2=2\pi r_2=\pi D_2 \\ {r}_2=o_2/(2\pi )=400/(2\cdot 3.1416)=63.662\text{cm} \end{gathered}$$

$o_1=2\pi \cdot r_1=2\cdot 3.1416\cdot 11.2838=70.8982\text{cm}$

$S_2=\pi \cdot r_2^2=3.1416\cdot 63.662^2=12732.3954{\text{cm}}^2$

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