Mice

Mice consumed a circular hole in a slice of cheese. The cheese is a circular cut with a radius of 20 cm and an angle of 90 degrees. What percentage of the cheese ate mice if they made 20 holes with a diameter of 2 cm?

Correct answer:

f =  20 %

Step-by-step explanation:

$$\begin{gathered} r=20\text{cm} \\ {D}_2=2\text{cm} \\ {r}_2=D_2/2=2/2=1\text{cm} \\ n=20 \\ \alpha =90{}^{\circ } \\ S=\pi \cdot r^2\cdot \frac{\alpha }{360}=3.1416\cdot 20^2\cdot \frac{90}{360}\doteq 314.1593{\text{cm}}^2 \\ {S}_2=n\cdot \pi \cdot r_2^2=20\cdot 3.1416\cdot 1^2\doteq 62.8319{\text{cm}}^2 \\ f=100\cdot \frac{S_2}{S}=100\cdot \frac{62.8319}{314.1593}=20\% \end{gathered}$$

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