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Math Help - Finding the diameter of a slice of a sphere

  1. #1
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    Cool Finding the diameter of a slice of a sphere

    Hi there, this is really a practical application question as I am building something and want to make the slice only once.

    I have a sphere of known circumference - 56.5cm
    At exactly 1 cm height from the bottom of the sphere, what is the diameter / circumference of the sphere?
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  2. #2
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    Re: Finding the diameter of a slice of a sphere

    Quote Originally Posted by Pinkypinks View Post
    Hi there, this is really a practical application question as I am building something and want to make the slice only once.

    I have a sphere of known circumference - 56.5cm
    At exactly 1 cm height from the bottom of the sphere, what is the diameter / circumference of the sphere?
    The wording of the question is quite confusing ...

    - what is the bottom of a sphere?
    - why should the diameter (or the circumference) change?

    Obviously the radius is nearly 9 cm.
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  3. #3
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    Re: Finding the diameter of a slice of a sphere

    Quote Originally Posted by Pinkypinks View Post
    I have a sphere of known circumference - 56.5cm
    At exactly 1 cm height from the bottom of the sphere, what is the diameter / circumference of the sphere?
    I assume that you are looking at the cross-section of the sphere at a height 1cm above the base. This cross-section is a circle, whose radius you can find by Pythagoras' theorem.

    The radius of the sphere is ~8.99cm. The radius of the circular cross-section is \sqrt{8.99^2 - 7.99^2}\approx 4.12cm, so its diameter is twice that (and its circumference is 2π times the radius, or ~25.9cm).
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    Re: Finding the diameter of a slice of a sphere

    Yes let me try and rephrase this

    what I meant to ask what is the diameter / circumference of the circle made from a slice 1cm from the bottom of a sphere of known circumference of 56.5cm.

    So conceptually, take a sphere, chop a slice 1cm thick off the top of it. What is the radius of the remaining top slice? (not the sphere as a whole)
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  5. #5
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    Re: Finding the diameter of a slice of a sphere

    Quote Originally Posted by Pinkypinks View Post
    Yes let me try and rephrase this

    what I meant to ask what is the diameter / circumference of the circle made from a slice 1cm from the bottom of a sphere of known circumference of 56.5cm.

    So conceptually, take a sphere, chop a slice 1cm thick off the top of it. What is the radius of the remaining top slice? (not the sphere as a whole)
    Draw a sketch.

    All calculations (see Opalg's post) take place in the (greyed) right triangle.
    Attached Thumbnails Attached Thumbnails Finding the diameter of a slice of a sphere-kugelkappe.png  
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