Lathe

From the cube of edge, 41 cm was a lathed maximum cylinder. What percentage of the cube is left as waste after being lathed?

Correct answer:

p =  21.5 %

Step-by-step explanation:

a=41 cm V1=a3=413=68921 cm3 V2=π⋅ (a/2)2⋅ a=3.1416⋅ (41/2)2⋅ 41≐54130.4268 cm3  p=100⋅ V1−V2V1=100⋅ 68921−54130.426868921=21.5%a = 41 \ \text{cm} \ \\ V_{1} = a^3 = 41^3 = 68921 \ \text{cm}^3 \ \\ V_{2} = \pi \cdot \ (a/2)^2 \cdot \ a = 3.1416 \cdot \ (41/2)^2 \cdot \ 41 \doteq 54130.4268 \ \text{cm}^3 \ \\ \ \\ p = 100 \cdot \ \dfrac{ V_{1}-V_{2} }{ V_{1} } = 100 \cdot \ \dfrac{ 68921-54130.4268 }{ 68921 } = 21.5 \%

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