1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

2. Geometry of 3D Solids
Geometry is the study of points, lines, planes, surfaces and solids.
No Dimensions
One Dimension
Two Dimensions
Three Dimensions
Point
Line
Plane
Solid

3. Geometry of 3D Solids
All the faces of a solid together make up the surface of the solid. A face of the solid may be plane or curved. A cuboid has 6 plane faces.
A vertex is a point where three or more edges meet. This cuboid has 8 vertices.
An edge is a line segment where two faces of a solid meet. This cuboid has 12 edges. The edges form the framework of the solid.

4. Geometry of 3D Solids There are two groups of solids:
Solids with all faces plane (e.g. prisms or pyramids)
Solids with at least one curved face (e.g. cylinder, cone, sphere)

5. Geometry of 3D Solids
A prism is a solid geometric figure whose two ends are similar, equal and parallel polygon shapes, and whose sides are parallelograms.
Recall that two figures with the same shape and size are said to be congruent. Thus, the end faces of prisms are congruent.
In a right prism the end faces are the same shape and size and parallel. All other faces are rectangles that are perpendicular to the end faces.

6. Geometry of 3D Solids
In Math Studies we will only investigate right prisms.

7. Geometry of 3D Solids
Some right prism we will investigate:

8. Geometry of 3D Solids
If you cut parallel to the end faces in a right prism, the cross-section will always be the same shape and size.

9. Geometry of 3D Solids
The base of a pyramid is a polygon. The other faces are triangles that meet at a point called the apex. In a right pyramid the apex is vertically above the center of the base.

10. Geometry of 3D Solids
The cross-sections parallel to the base of a pyramid are the same shape as the base, but different sizes.

11. Geometry of 3D Solids Solids with at least one curved face:
Sphere: contains one curved face

12. Geometry of 3D Solids Solids with at least one curved face:
Hemisphere: has two faces, one plane and one curved.

13. Geometry of 3D Solids Solids with at least one curved face:
Cylinder: has three faces, two plane and one curved.

14. Geometry of 3D Solids Solids with at least one curved face:
Cone: has two faces, one plane and one curved.

15. Geometry of 3D Solids
In Math Studies we will only study right cones. In a right cone:
the apex is vertically above the center of the base.
the vertical height (h) is the distance from the apex to the center of the base.
the slant height (l) is the distance from the apex to any point on the circumference of the base.

16. Practice For each of these solids: Write down its name.
Write down the number of faces, edges and vertices.
Write down the number of plane faces and curved faces.