# Cutting square

From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?

Result

p =  78.54 %

#### Solution:

$a = 30 \ cm \ \\ r = a/2 = 30/2 = 15 \ cm \ \\ S_{ 1 } = a^2 = 30^2 = 900 \ cm^2 \ \\ S_{ 2 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 15^2 \doteq 706.8583 \ cm^2 \ \\ \ \\ p = 100 \cdot \ \dfrac{ S_{ 2 } }{ S_{ 1 } } = 100 \cdot \ \dfrac{ 706.8583 }{ 900 } \doteq 78.5398 = 78.54 \%$

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