Aria laterala a unui con circular drept este 72 radical din 2 pi, iar unghiul de la vf conului dintre doua generatoare opuse este 90 grade. Det. volumul conului
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Al=πrG
Fie ΔAVB dreptunghic isoscel , m(∡V)=90°=>m(∡A)=m(∡B)=45°
VA=VB=G
AB=2r
In ΔVAB ,m(∡V)=90°=>sinB=G/2r=>G=2r*sinB=2r√2/2=r√2
Al=πr²√2=>πr²√2=72√2π=>r²=72=>r=6√2
G=r√2=6√2*√2=6*2=12
Fie VO⊥AB=>VO inaltime H
AO=OB=r=6√2
In ΔVAO , m(∡O)=90°=>sinA=H/G=>H=GsinA=12*√2/2=6√2
V=πr²H/3=6√2*(6√2)²π/3=2√2*36*2π=144√2π