1. LESSON If the height of a regular square prism is 29 thumbs and the base edges are 40 thumbs, find the surface area and the volume. 7,840 thumbs 2 46,400 thumbs 3 Find the volume and the surface area of a regular hexagonal right prism with a height of 10 and a base edge of 6. Examples:

2. LESSON Examples:

3. LESSON cross section- the intersection of a solid with a plane The volume of a prism or a cylinder is equal to the product of the figure’s cross- sectional area and its height. where ₵ is the area of a cross section and h is the height

4. LESSON Concept

5. LESSON Example 3 Find the volume of the oblique cylinder to the nearest tenth. ≈ 17,671.5 cubic feet

6. LESSON Example 4 Find the volumes of the composite solids. S = 7200 + 540π in 3 ≈ 8896 in 3 30” 20” 12” 20’ 10’ 30’ S = 2250π ft 3 ≈ 7069 ft 3

7. LESSON Today: Answers to notes Warm-up 12.5 Instruction Warm-up: Find the volume of the prism.

8. LESSON 12.5 Volumes of Pyramids and Cones Objective: 1.Find volumes of pyramids. 2.Find volumes of cones. Vocabulary: none

9. LESSON The volume of a pyramid is equal to one third of the product of the height and the area of the base. where B is the area of the base and h is the height REMINDER: S pyramid = L + B h l V pyramid = Bh

10. LESSON The volume of a cone is equal to one third of the product of the height and the area of the base. where B is the area of the base and h is the height REMINDER: S cone = L + B V cone = Bh l

11. LESSON If the slant height of a regular square pyramid is 29 thumbs and the base edges are 40 thumbs, find the surface area and the volume. S= 3,920 thumbs 2 V = 11,200 thumbs 3 Examples:

12. LESSON If a cone has a height of 35 cornnuckles and diameter of 24 cornnuckles. Find the surface area and volume of this cone. S= 588π c 2 V = 1680π c 3 Examples:

13. LESSON k In a pyramid or a cone, the ratio of the area of the base to a cross section equals the square of the ratio of the figures’ respective distances from the vertex. Where  is the area of the cross section, B is the area of the base, k is the distance from the vertex to the cross section, and h is the height of the pyramid or cone. m n h

14. LESSON Find the area of the cross section to the nearest square pluck if the cross section is 25 plucks from the top? 361 plucks 2 Examples: 30 45 25 18u 2 8u 2 27u 2

15. LESSON Concept

16. LESSON Assignment Due tomorrow: 12.5 P. 876 #11-23 odd, 26-29, 32-34 – you must show work including formulas! Exit slip: Do the extra problems!