1. POLYGONS A polygon is a 2-dimensional shape made of straight lines. Examples: (only a few)

2. In this lesson, among others, we are going to study SOLIDS and more specific PRISMS. Definition:  A PRISM is a 3-dimensional solid with two identical bases.  The cross-section all along its length is the same everywhere. (uniform cross-section.)  A prism is named according to the shape of its base. (TRIANGULAR PRISM in this case.)

3. VOLUME FORMULAE: 1. CUBE: X

4. 2. RECTANGULAR PRISM: VOLUME FORMULAE:

5. 3. TRIANGULAR PRISM: VOLUME FORMULAE:

6. 4. CYLINDER: Did you notice that the volume of a right prism = area of the base x height? VOLUME FORMULAE:

7. EXAMPLE 1 Determine the volume of the cube with side 2,1 m. ANSWER If approximation is not specified, it can be done to any decimal, otherwise as requested.

8. EXAMPLE 2 Determine the volume of the cylinder with (Give your answer in terms of ). Key: h: height d: diameter

9. ANSWER Answer approximated to one decimal numbers. First determine h.  Volume is indicated as cubic units.  Answer is in terms of

10. EXAMPLE 3 Determine the volume of the triangular prism. ANSWER Height of is 8 cm.

11. EXAMPLE 4 A contractor has to build a solid staircase as indicated in the sketch. All the lines and planes meet at right angles and all the stairs have the same measurements. Determine how many cubic metres concrete is needed to build the staircase.

12. ANSWER Consider each step as a rectangular prism with and Length: STEP 1 = AB STEP 2 = CD STEP 3 = EF STEP 4 = GH

14. The contractor needs half a cubic metre of concrete to build the staircase. (Approximated to one decimal figure).

15. A cylindrical hole is drilled through a solid rectangular metal block as indicated in the sketch. Calculate the volume of the remaining metal. EXAMPLE 5

16. ANSWER

17. Determine the volume of the space inside the mailbox. EXAMPLE 6 A mailbox consists of half a cylinder on top of a rectangular prism, with measurements as indicated in the sketch.

18. ANSWER

19. EXERCISE 1 Determine the volume of each of the following solids: (Approximate your answer to one decimal figure.) 1. 2. The 2 base surfaces are quarter circles.

20. 3. Half a cylinder is cut from a rectangular prism.

21. 4. A cylindrical hole is cut out exactly in the middle of a cylinder. Diameter of inner cylinder is 10 mm.