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napkin ring problem

by Rozella Wisoky IV Published 3 years ago Updated 3 years ago

The napkin ring problem states that if you have two spheres, one small and one large, and you cut a hole in each of them so that they are of equal heights, the volume of each will be equal.

Full Answer

What is the napkin ring problem?

What happens to the radius of a sphere when the radius of the sphere shrinks?

About this website

What is the napkin ring paradox?

0:523:31What is the Napkin Ring Paradox? (And How Does it Work?) - YouTubeYouTubeStart of suggested clipEnd of suggested clipHigh you're left with two seemingly different napkin rings except they have the exact. Same internalMoreHigh you're left with two seemingly different napkin rings except they have the exact. Same internal volume. This is called the napkin ring paradox.

How do you find the volume of a napkin ring?

If the removed cylinder has height 2h and radius a, then the napkin ring has volume 4/3 PI h^3.

Why do napkin rings have the same volume?

Both frui rings have the same height, and therefore the same volume. Fruit image sources here and here. To see why, let's compare ring of height 2H with a sphere of radius H. The sphere is a degenerate ring — the hole through the centre has a radius of zero (Figure 2).

Should I use napkin rings?

Due to the historical significance of napkin rings, they should not be used in formal dining settings. However, if you think they give an added flair of personality to your table setting, consider using them only for casual dining or informal occasions.

Which is the correct formula in finding the volume of a cylinder?

π r2 hSolution: We know the volume of a cylinder is given by the formula – π r2 h, where r is the radius of the cylinder and h is the height.

What is volume of the sphere?

The formula for the volume of a sphere is V = 4/3 πr³.

What is a napkin ring called?

The napkin ring, occasionally called a serviette ring, was originally used to identify the napkins of a household between weekly wash days.

Where do you place a napkin ring?

0:070:53How to Place a Napkin Ring Accessory Around Your Linen RentalYouTubeStart of suggested clipEnd of suggested clipPick up the napkin ring. And place the napkin ring about halfway down the napkin. And open up andMorePick up the napkin ring. And place the napkin ring about halfway down the napkin. And open up and spread out the layers of the napkin.

Where do you place a napkin ring on the table?

Napkin Rings. If a napkin ring is present, after removing your napkin, place the ring to the top-left of the setting. At the end of the meal, grasp the napkin in the center, pull it through the ring, and lay it on the table with the point facing the center of the table.

Should napkin rings match silverware?

Napkin ring can also be matched with other accessories on the table like silverware, dinner set, spoon stand, placemats, etc.

Attribution

This idea was inspired by Michael Stevens of the YouTube channel Vsauce. Here is a link to the video on the napkin ring problem: https://www.youtube.com/watch?v=J51ncHP_BrY

Description

This model was created for week 7 of the Ultimaker design engine challenge. The challenge card is: Challenge card #1 - "Eureka!" Design an object that expresses the beauty of math. the two parameter cards are: Parameter Card #1 - Complex and Parameter Card #2 - Private.

Issues

Issues are used to track todos, bugs or requests. To get started, you could create an issue.

What is the napkin ring problem?

In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere.

What happens to the radius of a sphere when the radius of the sphere shrinks?

As the radius R of the sphere shrinks, the diameter of the cylinder must also shrink in order that h can remain the same. The band gets thicker, and this would increase its volume. But it also gets shorter in circumference, and this would decrease its volume. The two effects exactly cancel each other out.

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