Square metal sheet

We cut out four squares with a 300 mm side from a square sheet metal plate with a side of 0.7 m. Express the fraction and the percentage of waste from the square metal sheet.

Final Answer:

f =  13/49
p =  26.5306 %

Step-by-step explanation:

$$\begin{gathered} a=0.7\text{m} \\ b=300\text{mm}\to \text{m}=300:1000\text{m}=0.3\text{m} \\ {S}_1=a^2=0.7^2=\frac{49}{100}=0.49{\text{m}}^2 \\ {S}_2=4\cdot b^2=4\cdot {\frac{3}{10}}^2=\frac{9}{25}=0.36 \\ o=S_1-S_2=\frac{49}{100}-\frac{9}{25}=\frac{49}{100}-\frac{36}{100}=\frac{49-36}{100}=\frac{13}{100}=0.13{\text{m}}^2 \\ f=\frac{o}{S_1}=\frac{\frac{13}{100}}{\frac{49}{100}}=\frac{13}{49}=0.2653 \end{gathered}$$

$p=100\cdot f=100\cdot \frac{13}{49}=\frac{100\cdot 13}{49}=\frac{1300}{49}=\frac{1300}{49}\%=26.5306\%$

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