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# Volume of a sphere

AP.BIO:
ENE‑1 (EU)
,
ENE‑1.B (LO)
,
ENE‑1.B.1 (EK)
CCSS.Math:

## Video transcript

find the volume of a sphere with the 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 its or 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 we prove 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 of the radius of the sphere the radius of the sphere is half of the diameter so in this example our radius is going to be 7 centimeters 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 over 7 but we'll actually just get the calculator out to get the exact value for this volume so this is going to be this is going to be so my volume is going to be 4/3 and then I don't want to just put a PI there because that might interpret it as 4/3 PI so 4/3 times pi times pi times times 7 to the third power and order of operations it'll do the exponent before it does the multiplication so this should work and the units are going to be in centimeters cubed or cubic centimeters so we get 14 36 they don't tell us what to round it to so I'll just round it to the nearest 10th 14 36.8 so this is equal to four one thousand four hundred thirty six point eight centimeters cubed and we're done
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