Axial section of the cone

The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.

Correct result:

V =  366.4297 cm3

Solution:

D:s=2:3 S=312 cm2  2r:s=2:3 r:s=1:3  3r=s  S=πr(r+s) S=πr(r+3r) S=4 πr2  r=S4π=3124 3.14164.9828 cm D=2 r=2 4.98289.9656 cm s=3 r=3 4.982814.9484 cm   Verifying Solution:  k=D/s=9.9656/14.9484=230.6667  h=s2r2=14.948424.9828214.0935 cm  S1=π r2=3.1416 4.98282=78 cm2  V=13 S1 h=13 78 14.0935=366.4297 cm3



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