Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.

Correct answer:

V =  1521.6904 cm3
S =  774.5663 cm2

Step-by-step explanation:

h=10 cm r=8 cm n=5  a=2⋅ r⋅ sin(π/n)=2⋅ 8⋅ sin(3.1416/5)≐9.4046 cm h1​=r2−(a/2)2​=82−(9.4046/2)2​≐6.4721 cm  S1​=n⋅ 2a⋅ h1​​=5⋅ 29.4046⋅ 6.4721​≐152.169 cm2  V=S1​⋅ h=152.169⋅ 10=1521.6904 cm3
S=2⋅ S1​+n⋅ a⋅ h=2⋅ 152.169+5⋅ 9.4046⋅ 10=774.5663 cm2

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