Max - cone

From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone.
a) Calculate cone volume.
b) Calculate the waste.

Result

V =  100.64 cm3
x =  322.01 cm3

Solution:

V1=13π(min(6.2,10)/2)26.2=62.3941244954 cm3 V2=13π(min(10,6.2)/2)26.2=62.3941244954 cm3 V3=13π(min(6.2,6.2)/2)210=100.63568467 cm3 V=max(V1,V2,V3)=100.64 cm3V_1 = \dfrac13 \pi (\min(6.2, 10)/2)^2 \cdot 6.2 = 62.3941244954 \ cm^3 \ \\ V_2 = \dfrac13 \pi (\min(10, 6.2)/2)^2 \cdot 6.2 = 62.3941244954 \ cm^3 \ \\ V_3 = \dfrac13 \pi (\min(6.2, 6.2)/2)^2 \cdot 10 = 100.63568467 \ cm^3 \ \\ V = \max(V_1,V_2, V_3) = 100.64 \ \text{cm}^3
x=6.2 10 6.262.3941244954=322.01 cm3x=6.2 \cdot \ 10 \cdot \ 6.2- 62.3941244954=322.01 \ \text{cm}^3



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