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Math Help - trigonometry/ circle results help

  1. #1
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    trigonometry/ circle results help

    hello,

    A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

    answer: 25π/6 cm^2
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  2. #2
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    Quote Originally Posted by maay View Post
    hello,

    A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

    answer: 25π/6 cm^2
    The surface area of the cone is the same as the area of the sector.

    Since the angle is \frac{\pi}{3}, and a full circle is 2\pi, this means that you have

    \frac{\frac{\pi}{3}}{2\pi} = \frac{1}{6} of the circle.


    So A = \frac{1}{6}\pi r^2

     = \frac{1}{6} \pi(5\,\textrm{cm})^2

     = \frac{25\pi}{6}\,\textrm{cm}^2.
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  3. #3
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    Hello maay
    Quote Originally Posted by maay View Post
    hello,

    A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

    answer: 25π/6 cm^2
    The formula for the curved surface area of a cone is:
    A = \pi r l
    where r is the radius and l the slant-height of the cone.

    So if the radius of the original cardboard circle is 5 cm, can you see that this means that l = 5 when the cardboard is formed into a cone?

    So you can now:

    • Use the formula above to find r, given that A = \frac{25\pi}{6}


    • Use Pythagoras' Theorem to find h, the vertical height of the cone.


    • Use the formula V = \tfrac13\pi r^2h to find the volume of the cone.

    Can you complete it now?

    Grandad
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