Largest possible cone

It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, 7.2 cm.
a) Calculate its volume.
b) Calculate the waste.

Correct result:

V =  43.4294 cm3
x =  150.1066 cm3

Solution:

a=5.6 cm b=4.8 cm c=7.2 cm  r1=min(b/2,a/2)=min(4.8/2,5.6/2)=125=2.4 cm h1=c=7.2=365=7.2 cm V1=13 π r12 h1=13 3.1416 2.42 7.243.4294 cm3  r2=min(a/2,c/2)=min(5.6/2,7.2/2)=145=2.8 cm h2=b=4.8=245=4.8 cm V2=13 π r22 h2=13 3.1416 2.82 4.839.4081 cm3  r3=min(b/2,c/2)=min(4.8/2,7.2/2)=125=2.4 cm h3=a=5.6=285=5.6 cm V3=13 π r32 h3=13 3.1416 2.42 5.633.7784 cm3  V1>V2>V3 V=V1=43.4294=43.4294 cm3
K=a b c=5.6 4.8 7.2=193.536 cm3  x=KV=193.53643.4294=150.1066 cm3



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