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Solids
Group the solids in the image according to their characteristics.
Solids can be grouped based on their colour, shape, material, etc.
Like plane figures, solids can be grouped according to whether they are convex or concave.
Convex solids, concave solids
A solid is convex when every point on any line segment connecting two points of the solid lies within the solid.
A solid is concave if there is a line segment connecting two points of the solid that does not entirely lie inside the solid.
Solids can also be grouped based on the type of surfaces bounding them.
Solids bounded by curved surfaces
The sphere is a solid bounded by curved surfaces.
A spherical surface, or simply a sphere, is a set of points found at the same distance from a given point in space.
The given point is the centre \latex{ (O) } of the sphere, while the distance is its radius \latex{ (r) }.
The radius is a line segment connecting the centre and any point of the spherical surface.
The diameter is a line segment passing through the centre that connects two points of the spherical surface. Symbol: \latex{ d }.
The diameter of the sphere is twice the \latex{ (d = 2 \times r) }.
The word sphere may refer to the spherical surface and the solid itself.
radius \latex{ (r) }
centre \latex{ (O) }
diameter \latex{ (d) }
Solids bounded by curved and flat surfaces
Solids bounded by flat surfaces
Solids with only flat surfaces are called polyhedra.
Polyhedra are bounded by faces.
The intersections of faces are called edges.
The edges intersect at vertices.
The intersections of faces are called edges.
The edges intersect at vertices.
vertex
edge
face
Exercises
{{exercise_number}}. How many faces, edges and vertices do these solids have? How many of each polygon are these solids bounded by?
b)
a)
c)
d)
{{exercise_number}}. Which solids are convex, and which ones are concave?
{{exercise_number}}. How many faces, edges and vertices do these solids have? How many of each polygon are these solids bounded by?
b)
a)
c)
d)
{{exercise_number}}. At least by how many flat surfaces is a solid bounded?
{{exercise_number}}. Is the solid missing from the cube concave or convex?
b)
a)
c)
{{exercise_number}}. One of the parts of the cubes has been cut off by a plane.
a) How many edges, faces and vertices do the following solids have?
b) How many edges, faces, and vertices does the solid that has been cut off have?
b) How many edges, faces, and vertices does the solid that has been cut off have?
b)
a)
c)
d)
e)
Quiz
How can you make four congruent triangles using six matches, so that every side of every triangle is one matchstick long?
