Lathe

Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.

Correct result:

p =  21.5 %

Solution:

p=100%⋅V1−V2V1=100%⋅533−π5324⋅53533=100⋅(1−π4)=21.5%p = 100\% \cdot \dfrac{ V_1-V_2}{ V_1} = 100\% \cdot \dfrac{ 53^3-\pi \dfrac{ 53^2}{4} \cdot 53 }{ 53^3} = 100 \cdot (1- \dfrac{ \pi}{4} ) = 21.5 \%

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