Quadrilateral 23891

A cylinder with the maximum possible base was ground from a wooden regular quadrilateral prism (edge 2.8 cm, height 7.5 cm). What percentage of the material was wasted as waste? What percentage would it be if the height of the prism were twice as large?

Correct answer:

p =  21.4602 %
p₂ =  21.4602 %

Step-by-step explanation:

$$\begin{gathered} a=2.8\text{cm} \\ {S}_1=a^2=2.8^2=\frac{196}{25}=7.84{\text{cm}}^2 \\ r=a/2=2.8/2=\frac{7}{5}=1.4\text{cm} \\ {S}_2=\pi \cdot r^2=3.1416\cdot 1.4^2\doteq 6.1575{\text{cm}}^2 \\ p=100\cdot \frac{S_1-S_2}{S_1}=100\cdot \frac{7.84-6.1575}{7.84}=21.4602\% \end{gathered}$$

$p_2=p=21.4602=21.4602\%$

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