Definition
Sphere
A sphere is a three-dimensional curved surface whose points are all equally far from its centre.
What it means
A sphere is perfectly round in every direction. From the centre, every point on its surface is the same distance away. It has no flat faces, edges, or vertices.
Remember it
One centre, one radius, round in every direction.
Example
A sphere has centre O and radius 5 cm. Point A is 5 cm from O, so A lies on the sphere. Point B is 3 cm from O, so B lies inside the ball, not on the sphere.
Watch for
A circle is flat and two-dimensional; a sphere is a three-dimensional surface.
Common mix-up
In everyday primary lessons, “sphere” may name the solid object. Exact geometry separates the surface, called the sphere, from the filled ball.
Exact meaning
In exact geometry, a sphere is the set of all points in three-dimensional space that are exactly one radius from a chosen centre. A solid ball includes the sphere and all points inside it.