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Example Question #13 : How To Find The Volume Of A Sphere
is a point on a sphere, and
is the point on the sphere farthest from
. The shortest curve from
to
that is completely on the sphere is
in length.
Give the volume of the sphere.
The figure referenced is below. is the center of the sphere.
The shortest curve connecting to its opposite point
is a semicircle. Also,
is a diameter of the sphere, and
and
are radii.
Given radius , a semicircle has length
Setting and solving for
:
.
The volume of a sphere, given its radius , is
.
Setting :
Example Question #121 : Solid Geometry
Find the volume of a sphere whose diameter is 10cm.
Radius is half of the diameter. Half of 10cm is 5cm.
Example Question #42 : Spheres
The radius of the sphere shown here is long. What is its volume?
The formula for the volume of a sphere given its radius
is
The radius is stated to be long; hence, we can calculate the sphere's volume by substituting this value for
into the formula, as shown:
Hence, the volume of the sphere is
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