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Geometry: Volume-Right Circular Cone & Sphere
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Right Circular Cone
A right circular cone is a cone whose axis is a line segment joining the vertex to the midpoint of the circular base.
       Volume of the cone = 1/3r2h
where r is the radius and h is the height of the cone.

The set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre) forms a sphere.
      Volume of the sphere = 4/3 R3
where R is the radius of the sphere.
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Example: A right circular cone is of height 12cm and the radius of its base is 3cm. It is melted and recast into a sphere. Find the radius of the sphere.
Solution: Given:
r = radius of the base of the cone = 3 cm
h = Height of the cone = 12 cm
              Volume of the cone = 1/3r2h = 1/3 x x 32 x 12 cm3

Now let R cm be the radius of the sphere obtained by recasting the melted cone. So,
Volume of the sphere = 4/3 R3

As volume of the material in the form of sphere and cone remains the same.
4/3 R3 = 1/3 x x 32 x 12
R3 = [32 x 12]/4 = 33
R = 3
Hence, radius of the sphere is 3 cm.
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