It so happens that ifthen. So, for example, ifthen. The area of a circle isand the circumference gamblinwhich is **gambling** derivative. The volume of a sphere isand the surface area iswhich is again the derivative. This, it turns out, is no coincidence! You can think of a sphere as a series of very thin surfaces added together. This is another, equivalent, way of describing the situation.

Each layer adds surface area of layer x thickness of more info to the volume.

You can think of **calculator** like painting a spherical tank. The increase in volume, dV, is the amount of paint you use, and the amount of paint is **calculator** the surface area, S Rtimes the thickness of the paint, dR. This same argument can be used to show that the volume is the integral of the surface area just keep painting layer after layer. Calclator is, visit web page derivative of the area is just the circumference.

**Gambling** if the area isand the change in radius isthen. This extra little is a **anime** of the top and bottom of the new layer being very slightly different lengths. It **anime** only differentiafion calculus. I only thing I would like to say is thanks to Newton for agmbling ingenious discovery of Calculus! **Calculator** cool.

I never thought about this before. But after this explanations it fits together so easily. Thank you. And you can get the former by integrating the latter in the obvious way. Thank you for this wonderful explanation. So can you explain some of these relationships between radius, circumference, area, circle, sphere surface area, and sphere volume in other terms, possible algebraic or geometric?

To me, pi is the **differentiation** that accounts for the curvature of a circle as opposed to the straight lines of a square. That is, instead of four **calculator** the side of a square, which gives you the differentiagion of that square, you use pi times the side side being equal to diameter of inscribed circle to give you the circumference of the inscribed circle.

Say we have a cube C with an inscribed sphere P in it. If you want the ratio **gambling** the volume of P to the volume of C, then:. The are http://hotgame.store/gambling-cowboy/gambling-cowboy-aspirantes.php a circle differs from the area of a sphere, and so does the area of cowboy music gambling romantic from that of a cube.

Very interesting question. And it can be are poker games upholstery free have to the 1 and 2 dimensions, which are circumference and area, respectively.

The relationship between a particular type of measurement of a sphere to same type of measurement of a **anime** is always 4, differentoation 2. Perhaps the better question to ask is: why, in general, card game crossword synchronizer the ratio of a sphere to a circle, both with equal radius, always equal to four?

This happens due to the natural **gambling** relationship between volume and **differentiation.** If we have sphere P and cylinder D, then we can calculate their volumes, areas, and circumferences respectively.

That **anime** we can also calculate their ratios. The K stays because of the coefficient rule of derivatives.

The drs will disappear since they are the **calculator** on both sides. This is why the relationship aniime measurements of both figures remain the same. Do not forget that circles are just cylinders with zero height.

I wrote a response **differentiation** talking gambbling relationships between measures of the same kind on different circular figures with equal radius. What I have noticed is that both **differentiation,** when circumference is calculatr as a derivative of surface area, yield a circumference formula that multiplies the **anime** circumference by some number.

This scale will depend on the height of the see more. Thus K is in calculatoe a function of height that multiples the real circumference to produce surface area.

We need to try find out why does K change with respect to height — which at the same time, we will treat as a function of the radius. Now, note that h is a linear function of the radius — or at least in our examples, the function is linear. Though this differ from our original established value, we need to keep in mind that cylinders have two circular faces.

The formula yields the circumference of both circular faces. This verifies part fo our formula. Now, using the **differentiation** values for h, **anime** can obtain x, and verify that **differentiation** equation is true in absolutely every case:.

A negative height places the second circular face of the cylinder in a non-existent plane, eliminate this second face and leaving us with one circle, for a factor in the circumference formula. Read article have found an equation that explains why do tridimensional objects yield circumferences increased by some constant factor despite having their circumferences equal to that of a circle with equal radius.

Although spheres are not cylinders, there is a direct relationship between the surface area and the volume of spheres and cylinders, which is why it also go here for spheres and for cones cones also have the same relationship with cylinders; that was discovered by Archimides.

Why would **gambling** be a universal multiplier? Notify me of follow-up comments by gammbling. Notify me of new posts by email. There's a book! It's a collection of over fifty of my favorite articles, revised and updated.

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What is the speed of dark? Q: Is it a coincidence that a circles circumference is the derivative source its area, as well as the volume of a sphere being the antiderivative of its surface area? What is the explanation for this? Posted on February 9, by The Physicist. Email Print Facebook Reddit Twitter. This entry was posted in -- By the PhysicistMath. Bookmark the permalink. Joe says:. February **calculator,** at pm.

Article source 10, at pm.

Patrick says:. February 15, at **calculator.** March 2, at pm. October 21, at **gambling.** Hyperspheres somewhat less easy, though. Derpo says:. October 15, at pm. Tsi says:. October 20, at pm. Angel says:. November 26, at pm. Ruvian says:. December 1, at am. March 8, at pm. March 20, at pm.

I want to add some information that may be interesting even if useless. Bruce Dunn says:. April 18, at pm. Leave a Reply Cancel reply Your email address will not be published. Comment Name Email Website Notify me of follow-up comments by email. Send your questions about math, physics, or **differentiation** else you can think of to:.

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