Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.

Correct result:

V =  641.27 cm3
S =  516.1171 cm2

Solution:

a=9 cm S1=a2=92=81 cm2 s=a/2=9/2=92=4.5 cm h=2 s tan75=tan5π/12=23.75063 cm h2=h2+s2=23.75062+4.5224.1732 cm  V=13 S1 h=13 81 23.7506=641.27 cm3
S2=a h2/2=9 24.1732/2108.7793 cm2  S=S1+4 S2=81+4 108.7793=516.1171 cm2



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