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 result:

V =  1521.6904 cm3
S =  774.5663 cm2

Solution:

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)26.4721 cm  S1=n a h12=5 9.4046 6.47212152.169 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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