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March 24, 2017

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The sector shown is formed into a cone by joining its two radii. Calculate the volume of the cone correct to the nearest whole number.

It shows a diagram with a 240 degree sector or two-thirds of a circle with a radius of 12 cm.

How do I do this?
Thank you so much

  • geometry - ,

    Sometimes it helps to have an actual model of your problem.
    Take a piece of paper and cut out a sector approximating your given sector.
    Form it into a cone.
    You will see that the radius of the sector becomes the "slant height" of the cone, and the arc length of the sector becomes the circumference of the base of the cone.

    So, let's find the radius of the cone:
    The arc length of our sector would be 240/360 of the circumference of the circle from which the sector was obtained.
    so (240/36)( 24π) = 16π
    then for the base of the cone
    2πr = 16π
    r = 8
    Now we can find the height of the cone:
    h^2 + 8^2 = 12^2
    h = √80

    Volume of cone = (1/3) base x height
    = (1/3)(64π)(√80)
    = appr. 599 to the nearest whole number

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