2. Finding Volume of Solid Figures Ms. Julien East Cobb Middle School

3. First… What are we talking about when we talk about VOLUME of solid figures? a. The sound that comes from your TV or IPod b. The concept of having full, bouncy hair c. A collection of written documents (ie., newsletters, encyclopedias, etc.) d. The amount of space inside a solid figure

4. That’s right! Give yourself a pat on the back! Volume of a solid figure refers to the amount of space inside a solid figure.

5. What are some examples?? Water needed to fill a pool Water needed to fill a pool The amount of jelly inside a jar The amount of jelly inside a jar The amount of space inside a car’s trunk The amount of space inside a car’s trunk Air inside a mask Air inside a mask Clothes inside a suitcase Clothes inside a suitcase Ice cream inside a cone Ice cream inside a cone

6. Volume is measured in cubic units. This basically means that you are finding how many cubes you could fit inside the object.

7. So, what is the Volume of this Rectangular Prism? In other words, how many cubes could fit inside?

8. How did you get that answer? You multiplied 3 x 6, and then multiplied that product by 4. So, the volume of this rectangular prism is 72 cubic units.

9. Let’s analyze this to determine the formula… What does 3 6 give us? Area of the rectangular base, good! Then we multiplied the area of the base by the height This means we are basically “filling up” the figure, or finding the volume. V = l w h or V = Bh V = Area of the base x height

10. Volume Find the volume of this prism… Find the volume of this prism… Formula: V = B x h V = l x w x h 5 cm 4 cm 7 cm

11. Volume Find the volume of this prism… Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm 5 cm 4 cm 7 cm

12. Volume Find the volume of this prism… Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm V = 140cm 3 5 cm 4 cm 7 cm

13. Volume Volume of a Triangular Prism Volume of a Triangular Prism

14. Volume The same principles apply to the triangular prism. The same principles apply to the triangular prism. To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow). b h

15. Volume Now to find the volume… Now to find the volume… We must then multiply the area of the base (B) by the height (h) of the prism. This will give us the Volume of the Prism. B h

16. Volume Your turn… Your turn…Find the Volume

17. How can I find the volume of a square pyramid? Let’s Experiment!

18. Volunteers: 1. Compare the characteristics of the prism and the pyramid. (ie, length, width, height) 2. Fill the pyramid completely with water. 3. Dump the water from the pyramid into the prism. 4. Continue until the prism is full. 5. What do you observe? What do you think is the formula for volume of a pyramid?

19. Volume of a Pyramid (Area of Base x Height)  3 (Area of Base x Height) 1 3 click to reveal A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

20. Pyramids are named by the shape of their base.. The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h). V = Bh 1313 =5 m side length = 4 m V = Bh 1313

21. How can I find the volume of a square pyramid?

22. If you said V = 1/3 Bh … GOOD JOB!

23. So… what is volume? The amount of space, measured in cubic units, of a 3D solid figure.

24. Volume Formula Recap: Prisms: Prisms: V = Bh Pyramids: Pyramids: V = 1/3 Bh On all of these, B stands for “Area of the Base”. So, you must determine what shape the base is and use the correct formula to get the area of the base. Then, complete the formula. On all of these, B stands for “Area of the Base”. So, you must determine what shape the base is and use the correct formula to get the area of the base. Then, complete the formula.

25. You do not have to memorize these formulas… however, you must understand how to use them! In other words, if given a formula and the numbers you need for the variables (length, width, height, radius, etc.), could you find the volume of a rectangular prism, square pyramid, cylinder, or a cone?

26. 8 cm 7 cm 15.3 cm Find the volume

27. Find the Volume of a triangular pyramid with base edges of 8 in, base height of 4 in and a pyramid height of 10 in. 8 in 10 in 4 in

28. The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid.