Volume of a sphere
How can I find the volume of a sphere? Can you explain the
method clearly please?
The equation of a circle is
, where
is the radius.
So, at any point on the circle, and area of a disc enclosed by the circle is
.
Thus, summing up the discs of varying radii (corresponding to the equation),
we integrate:
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You didn't say how old you are, Danish.
Having looked up what school you are at, I suspect that you don't
know what integrate means.
The idea used above is one of splitting the sphere into lots and
lots of slices.
I expect you will be able to use the formula given at the end (r
is the radius of the sphere), but if you want to understand how
the formula comes about, there is an explanation of how to find
the volume of a sphere which you should be able to follow in two
articles on the NRICH site:
Volume of a pyramid and a cone
Mouhefanggai
These articles use the slicing idea, but do it in a way which
means you don't have to have studied A-level maths!
I'm only eleven but I know quite a lot for my age. I'm OK with
the formula for V.
Thanks
Danish,
Do you understand why the formula of a cone is
? If so, here is a treatment of the volume of sphere (due to
Archimedes).
Suppose you are given a right cone and a sphere, both of radius
(a right
cone is one which radius=height). If you take a slice through the sphere at
a distance
(
)above the equator, the radius of the
resulting circle isgiven by
. Also, if you take a slice through
the cone at a distance
from its vertex, then the radius of circle is just
. So the area of the two circle adds up toa circle of radius
. Then,
''summing up the slices'', you get
1/2 x Volume of sphere + Volume of rightcone =Volume ofcylinder
Substituting what we know:
1/2 x Volume of sphere of radius
and now just rearrange to give the volume of sphere is
.
Kerwin