Rectangle 4077

We cut the largest possible circle from a paper rectangle with 25 cm and 15 cm sides. How many % of the area of the rectangle is the area of the circle?

Correct answer:

p =  47.1239 %

Step-by-step explanation:

$$\begin{gathered} a=25\text{cm} \\ b=15\text{cm} \\ r=\min (a,b)/2=\min (25,15)/2=\frac{15}{2}=7.5\text{cm} \\ {S}_1=a\cdot b=25\cdot 15=375{\text{cm}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 7.5^2\doteq 176.7146{\text{cm}}^2 \\ p=100\cdot \frac{S_2}{S_1}=100\cdot \frac{176.7146}{375}=47.1239\% \end{gathered}$$

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