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

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
See also our right triangle calculator.
Tip: Our volume units converter will help you convert volume units.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: