Max - cone

The workshop must produce the greatest cone from the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, and 6.2 cm.
a) Calculate cone volume.
b) Calculate the waste.

Final Answer:

V =  100.64 cm³
x =  322.01 cm³

Step-by-step explanation:

$$\begin{gathered} V_1=\frac{1}{3}\pi (\min (6.2,10)/2{)}^2\cdot 6.2=62.394124495396c{m}^3 \\ {V}_2=\frac{1}{3}\pi (\min (10,6.2)/2{)}^2\cdot 6.2=62.394124495396c{m}^3 \\ {V}_3=\frac{1}{3}\pi (\min (6.2,6.2)/2{)}^2\cdot 10=100.63568466999c{m}^3 \\ V=\max (V_1,V_2,V_3)=100.64{\text{cm}}^3 \end{gathered}$$

$x=6.2\cdot 10\cdot 6.2-62.394124495396=322.01{\text{cm}}^3$

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