# Lathe

From the cube of edge, 37 cm was a lathed maximum cylinder. What percentage of the cube is left as waste after lathed?

Correct result:

p =  21.5 %

#### Solution:

$p=100\mathrm{%}\cdot \frac{{V}_{1}-{V}_{2}}{{V}_{1}}=100\mathrm{%}\cdot \frac{3{7}^{3}-\pi \frac{3{7}^{2}}{4}\cdot 37}{3{7}^{3}}=100\cdot \left(1-\frac{\pi }{4}\right)=21.5\mathrm{%}$

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