# 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 perimeter 400 cm.

Result

r1 =  11.284 cm
r2 =  63.662 cm
o1 =  70.899 cm
S2 =  12732.405 cm2

#### Solution:

$S_{ 1 } = 400 \ cm^2 \ \\ r_{ 1 } = \sqrt{ S_{ 1 }/\pi } = \sqrt{ 400/3.1416 } \doteq 11.2838 = 11.284 \ \text{ cm }$
$o_{ 2 } = 400 \ cm \ \\ r_{ 2 } = o_{ 2 }/(2 \pi) = 400/(2 \cdot \ 3.1416) \doteq 63.662 = 63.662 \ \text{ cm }$
$o_{ 1 } = 2 \pi \cdot \ r_{ 1 } = 2 \cdot \ 3.1416 \cdot \ 11.2838 \doteq 70.8995 = 70.899 \ \text{ cm }$
$S_{ 2 } = \pi \cdot \ r_{ 2 }^2 = 3.1416 \cdot \ 63.662^2 \doteq 12732.4046 = 12732.405 \ cm^2$

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