1. Volume of Geometric Solids
Geometry
Regular Program SY
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson

2. It refers to the measure of the amount of space contained in a solid.
The Geometric Solids
What is VOLUME?
It refers to the measure of the amount of space contained in a solid.
These solids take up space.

3. It refers to the measure of the amount of space contained in a solid.
The Geometric Solids
What is VOLUME?
It refers to the measure of the amount of space contained in a solid.
It is measured in cubic units.

4. Example:
How many cubes of cubic unit can fit inside the solid?

5. Example:
How many cubes of cubic unit can fit inside the solid?

6. Example:
How many cubes of cubic unit can fit inside the solid?

7. So how do we determine the volume of a solid?
It takes 3x3 cubes to cover the base area.
It takes 3x the base area to fill up the whole solid.
Height h
You need the base area h times.
Base area

8. VOLUME OF SOLIDS
PRISM
V = Base area x Height of prism
CYLINDER
V = Base area x Height of cylinder

9. Exercises on Volume Solve for the volume of each solid

10. Exercises on Volume Solve for the volume of each solid

11. Exercises on Volume Solve for the volume of each solid

12. Try these! Which has a greater volume?

13. Try these! Which has a greater volume?

14. Try these! Which has a greater volume?

15. Try these! Solve for the volume of each solid

16. Try these! Solve for the volume of each solid

17. VOLUME OF SOLIDS
PYRAMID
V = One-third of the volume of the prism with same base and height

18. VOLUME OF SOLIDS
CONE
V = One-third of the volume of the cylinder with same base & height

19. PRISM CYLINDER PYRAMID CONE
SUMMARY: VOLUME
VOLUME
PRISM x
CYLINDER
PYRAMID
CONE

20. Exercises on Volume Solve for the volume of each solid

21. Exercises on Volume Solve for the volume of each solid

22. Exercises on Volume Solve for the volume of each solid

23. Extra Exercises on Volume Solve for the volume of each given solid

24. Extra Exercises on Volume Solve for the volume of each given solid

25. Extra Exercises on Volume Solve for the volume of each given solid

26. Extra Exercises on Volume Solve for the volume of each given solid

27. Extra Exercises on Volume Solve for the volume of the liquid.

28. Extra Exercises on Volume Solve for the volume of the liquid.

29. Extra Exercises on Volume

30. Extra Exercises on Volume (seatwork) Solve the following:
1. Find the volume of an oblique prism inclined 45o from the base, if the area of the base is 20 cm2 and the lateral edge is 15 cm.
2. Find the volume of a right cylinder with a cylindrical hole if the larger radius is 10 inches, the smaller radius is 8 inches and the height is 9 inches.