geometry

A right circular cone is made from of a radius of 5 cm, a central angle of 216 degrees, what is the volume of the cone in cubic cm?

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  1. The key here is that the circumference of the base of the cone is equal to the arc length of the original sector.
    arc-length/10π = 216/360
    arc-length = 6π

    if radius of cone is r,
    2πr = 6π
    r = 3

    by taking a cross-section of the cone, we get a right-angled triangle with hypotenuse of 5, height of h and base segment of 3
    so h^2 + 3^2= 5^2
    h = 4

    vol of cone = (1/3)π(3^2)(4) = 12π cm^3

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