math

The angles of a triangle are in the ratio 1:2:3. If its hypotenuse is 12cm, find the volume of the double cone formed by revolution of triangle about its hypotenuse.

Pls help me!

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  1. x + 2x + 3 x = 180
    so
    x = 30
    we are talking about a 30, 60, 90 triangle
    sides are 6 and 6 sqrt 3

    bottom cone (I have the 6 side down)
    hypotenuse is 6
    length along axis = 6 sin 30 = 6/2 = 3
    length perp to axis = 3 sqrt 3
    volume of bottom cone
    = (1/3) 3 (pi) (3 sqrt3)^2
    = pi (9*3) = 27 pi

    top cone
    length along axis = 12-3 = 9
    same 3 sqrt 3 perp to axis
    Vol = (1/3)(9)(3 sqrt 3)^2
    = 81 pi

    total = (27+81)pi = 108 pi
    so I have a cone

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