Four circles

1) Calculate the circle radius if its area is 400 cm²
2) Calculate the radius of the circle whose circumference is 400 cm.
3) Calculate circle circumference if its area is 400 cm²
4) Calculate the circle's area if the perimeter is 400 cm.

Final 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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