# Thread: Finding the diameter of a slice of a sphere

1. ## 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?

2. ## Re: Finding the diameter of a slice of a sphere

Originally Posted by Pinkypinks
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.

3. ## Re: Finding the diameter of a slice of a sphere

Originally Posted by Pinkypinks
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 $\sqrt{8.99^2 - 7.99^2}\approx 4.12$cm, so its diameter is twice that (and its circumference is 2π times the radius, or ~25.9cm).

4. ## 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)

5. ## Re: Finding the diameter of a slice of a sphere

Originally Posted by Pinkypinks
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.

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### cross section of a sphere along its diameter

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