Nine-sided 36071

Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm

Correct answer:

S =  1526.4708 cm2
V =  3773.6434 cm3

Step-by-step explanation:

ρ=12 cm h=24 cm n=9 a=2 ρ tan(π/n)=2 12 tan(3.1416/9)8.7353 cm  S1=n 2a ρ=9 28.7353 12471.7054 cm2  h2=ρ2+h2=122+242=12 5 cm26.8328 cm  S2=2a h2=28.7353 26.8328117.1962 cm2  S=S1+n S2=471.7054+9 117.1962=1526.4708 cm2
V=31 S1 h=31 471.7054 24=3773.6434 cm3



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