Square metal sheet

Four squares of 300 mm side were cut out 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.

Correct result:

f =  0.2653
p =  26.5306 %

Solution:

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

$p=100\cdot f=100\cdot 0.2653={\displaystyle \frac{1300}{49}}=26.5306\mathrm{\%}$

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