Recognition of Solids
68. The Sphere's Secret · every surface point keeps the same distance
Every point on the surface is exactly one radius away from the centre.
A sphere is a perfectly round 3D solid where every point on the surface is the same distance (the radius r) from the centre. Examples: a ball, a globe, a marble.
What this lesson covers
Try to break it
Try dragging P around the circle. The radius OP stays exactly 200 units, just like the definition says. Try as you might, you can't break it — that's the power of a sphere!
How you build it
Construct a sphere with centre and radius.
- Mark the centre point O of the sphere.
- With centre O, draw the circle for the sphere's outer boundary.
- Draw a line from O to any point on the circle's edge. This is the radius.
The proof, step by step
Prove that every point on the sphere's surface is one radius from the centre.
- Drag point P around the entire circumference. Observe that the length of OP never changes, regardless of P's position.
Worked example
Which of the following best describes a sphere?
A sphere is defined as a round solid figure where every point on its curved surface is at the same distance (radius) from its centre.
- A solid with flat faces and sharp edges
- A round solid where every point on the surface is equidistant from the centre — correct
- A 2D shape with no thickness
- A solid with one vertex and one curved surface