Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.

Correct answer:

V =  121.0521 cm3

Step-by-step explanation:

h=5 cm S=140 cm2 S=2 6 S1+6ah  S=26a2sqrt(3)/4+6ah  140=2 6 a2 3/4+6 a 5 5.196152a230a+140=0 5.196152a2+30a140=0  p=5.196152;q=30;r=140 D=q24pr=30245.196152(140)=3809.84512 D>0  a1,2=2pq±D=10.39230430±3809.85 a1,2=2.88675158±5.9393896524105 a1=3.0526380716253 a2=8.8261412331956   Factored form of the equation:  5.196152(a3.0526380716253)(a+8.8261412331956)=0 a=a1=3.05263.0526 cm S1=a2 3/4=3.05262 3/44.0351 cm2 S2=6 a h=6 3.0526 591.5791 cm2 P=6 S1=6 4.035124.2104 cm2  V=P h=24.2104 5121.0521 cm3   Verifying Solution:  S3=2 P+S2=2 24.2104+91.5791=140 cm2

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