# 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:

$p=100\mathrm{%}\cdot \frac{{V}_{1}-{V}_{2}}{{V}_{1}}=100\mathrm{%}\cdot \frac{5{3}^{3}-\pi \frac{5{3}^{2}}{4}\cdot 53}{5{3}^{3}}=100\cdot \left(1-\frac{\pi }{4}\right)=21.5\mathrm{%}$

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