Three-dimensional shapes
Nearly everything that we can see and touch takes up space. These things are either gases, liquids or solids. You will study some of the properties of liquids and gases in science.
Most solids, or three-dimensional shapes, such as stones and trees, have rough and irregular shape. This usually occurs in nature. However, some three-dimensional shapes, such as tin, can and houses, have regular shapes. These are usually made by people. We often call then geometrical solids.
Look at the photograph below, it show groundnut pyramids
The diagram below show that each pyramid is made up from a square-based pyramid and a cuboid.
Cuboids and cubes
Look at a matchbox. The name of its shape is a cuboid
A face may be flat (plane) or curved. A cuboid has 6 plane faces. Each face is in the shape of a rectangle.
A rectangle
An edge is a line where two faces meet. It may be straight or curved. A cuboid has 12 straight edges.
A vertex is a point or corner where three or more edges meet The plural of vertex is vertices. A cuboid has 8 vertices.
Drawing cuboids
There are many ways of drawing cuboids. In each case it is impossible to show the solid as it really is. A skeleton view is very useful since it shows all the edges. The drawings below show how to draw a skeleton view very quickly. Notice that some edges are hidden from view. We usually show these as broken lines.
Cubes
A cube is a cuboid in which all six faces are squares
Exercise
Write down five everyday objects which are cuboids
Cylinders and prisms
Cylinder
The cylinder has two plane faces and one curved face. It has no vertices and two curved edges> the two plane faces are both circles.
A skeleton view of a cylinder is drawn in much the same way as that of a cuboid
Prism
The base and top faces of a prism are always the same shape. The names of prisms come from the shape of their base and top faces. The side faces of right prisms are always rectangular.
The cuboid is a rectangular prism and the cylinder can be thought of as a special prism.
Cones and Pyramids
Pyramid: A 3-dimensional solid in which the base is a polygon and the sides are triangles which meet in one point called the vertex. We shall examine regular pyramids in which the base is a regular polygon and the sides are congruent triangles.
A Right Circular Cone: A 3-dimensional solid in which the base is a circle. The side of a cone is formed by straight lines which connect the circular base to a vertex. The height is the perpendicular distance from the vertex to the base and meets the base in the center of the circle.
The Lesson:
The diagrams below show a pyramid and a cone. Both have a height of h and radius of r. In the pyramid at left, r is the radius of the regular hexagon that is the base of the pyramid. In the cone at right, r is the radius of the circular base. The slant height is s in both diagrams.
Sphere
Nearly every ball is sphere shaped
A tennis ball Outline of a ball; sphere
Half of a sphere is called a hemisphere
Test and Exercise
Write down five everyday objects each of which is either sphere-shaped or contains part of a sphere in its shape.
Which of the following solids will roll smoothly on a plane surface?
a. cube b. cone c. sphere d. cylinder e. cuboid
