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Volume of a sphere (video) | Khan Academy

You could view it as a globe of some kind. So I'm going to shade it a little bit so you can tell that it's three-dimensional. They're giving us the diameter. So if we go from one side of the sphere straight through the center of it.


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So we're imagining that we can see through the sphere. And we go straight through the centimeter, that distance right over there is 14 centimeters.

10 easy ways you can tell for yourself that the Earth is not flat

Now, to find the volume of a sphere-- and we've proved this, or you will see a proof for this later when you learn calculus. So they've given us the diameter. And just like for circles, the radius of the sphere is half of the diameter. So in this example, our radius is going to be 7 centimeters. And in fact, the sphere itself is the set of all points in three dimensions that is exactly the radius away from the center.

His estimate of , stadia 28, miles or 46, kilometers is close to Earth's actual circumference of 24, miles 40, kilometers if measured at the equator. Meet Earth's Orbital Dance Partner: The scientific basis for the Earth being a sphere is often misattributed to the era of Christopher Columbus, whose crew had feared they would sail over the edge of the planet, the myth goes.

In reality, Columbus, who would certainly have studied Aristotle, would have known full well that Earth is round. His expedition was initially controversial instead because the scientific advisers to King Ferdinand believed the journey west from Spain to India was too great a distance based on estimates of Earth's size. Flat Earth theory is a modern phenomenon, beginning in the s with the work of Samuel Birley Rowbotham, founder of the Zetetic Society, which would later inspire the Flat Earth Society in the 20th century, according to LiveScience.


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Earth looks and feels flat after all from our everyday, ground-level viewpoint. Rowbotham envisioned the planet as a disk with the sun, moon and stars all floating just a few hundred miles away. The Flat Earth Society believes gravity is an illusion, the space program is a hoax, and world governments are conspiring to keep the truth from surfacing for a still-undetermined reason. Simple observations have determined the shape of the Earth for thousands of years, and there's plenty more evidence to support that fact.

Gravity, time zones, GPS, air travel, telescope imagery of other planets in our solar system all point to a round Earth. This is exactly what a sphere is. So, this is a sphere of radius 5 centered at the origin.

Volume of cones, cylinders, and spheres

This is exactly what happens in a cone. Points in a vertical plane will do this. There are actually two ways to do this conversion.


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We will look at both since both will be used on occasion. Solution 1 In this solution method we will convert directly to Cartesian coordinates.

Five Ways You Can Tell for Yourself That the Earth is Not Flat

To do this we will first need to square both sides of the equation. Solution 2 This method is much shorter, but also involves something that you may not see the first time around.