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Сфера көлемі

Сфера көлемінің формуласы-V=4/3πr³.Сфераның диаметрі берілген мысалда қолданылатын формуланы қараңыз. Видео авторлары: Сал Хан және Монтерей Технологиялық Институты.

Видео транскрипті

Find the volume of a sphere with a diameter of 14 centimeters. So if I have a sphere-- so this isn't just a circle, this is a sphere. 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. 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. 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. But the formula for the volume of a sphere is volume is equal to 4/3 pi r cubed, where r is the radius of the sphere. 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. But with that out of the way, let's just apply this radius being 7 centimeters to this formula right over here. So we're going to have a volume is equal to 4/3 pi times 7 centimeters to the third power. So I'll do that in that pink color. So times 7 centimeters to the third power. And since it already involves pi, and you could approximate pi with 3.14. Some people even approximate it with 22/7. But we'll actually just get the calculator out to get the exact value for this volume. So this is going to be-- so my volume is going to be 4 divided by 3. And then I don't want to just put a pi there, because that might interpret it as 4 divided by 3 pi. So 4 divided by 3 times pi, times 7 to the third power. In order of operations, it'll do the exponent before it does the multiplication, so this should work out. And the units are going to be in centimeters cubed or cubic centimeters. So we get 1,436. They don't tell us what to round it to. So I'll just round it to the nearest 10th-- 1,436.8. So this is equal to 1,436.8 centimeters cubed. And we're done.