Recognition of Solids
114. The 3D Promise · Length, Breadth, Height — the solid's signature
The object always has three dimensions: length, breadth, and height.
A solid is any 3D object — it has length, breadth, and height. Solids occupy volume in space. Common solids: cubes, cuboids, spheres, cones, cylinders, prisms, pyramids.
What this lesson covers
Try to break it
What happens when you make the length zero? It becomes a 2D rectangle. A solid needs all three!
The proof, step by step
Prove that the object is a solid with length, breadth, and height.
- A straight line drawn on a flat sheet can only be measured in one way — along its length. So a line has 1 dimension.
- A rectangle on the same sheet can be measured two ways — length and breadth, at right angles. So a rectangle has 2 dimensions.
- A solid occupies space, so it can also be measured upward — its height — perpendicular to both length and breadth.
- Therefore the object can be measured along three independent directions; it is a solid with length, breadth, and height.
Worked example
Which of the following objects is a solid?
A brick is a solid because it has length, breadth, and height. A sheet of paper is 2D, a straight line is 1D, and a circle is 2D.
- A sheet of paper
- A brick — correct
- A straight line
- A circle