1. Students will be able to solve for perimeter, area and volume by…. 1. Finding the Perimeter & Area of Rectangles & Parallelograms 2. Finding the Perimeter and Area of Triangles and Trapezoids 3. Solving Right Triangles using the Pythagorean Theorem 4. Finding the Circumference and Area of Circles 5. Understanding How to Draw Three-Dimensional Figures 6. Finding the Volume of Prisms and Cylinders 7. Finding the Volume of Pyramids and Cones 8. Finding the Surface Area of Prisms and Cylinders 9. Finding the Surface Area of Pyramids and Cones 10. Finding the Volume and Surface Area of Spheres

2. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Learning Goal Assignment Learn to find the surface area of pyramids and cones.

3. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Pre-Algebra HOMEWORK Page 322 #1-6 Show Work!

4. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones 6-9 Surface and Area of Pyramids and Cones Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

5. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Warm Up 1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m. What is the surface area? 2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3.14 for . 2.48 m 2 1186.9 cm 2 Pre-Algebra 6-9 Surface and Area of Pyramids and Cones

6. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Problem of the Day Sandy is building a model of a pyramid with a hexagonal base. If she uses a toothpick for each edge, how many toothpicks will she need? 12

7. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Learning Goal Assignment Learn to find the surface area of pyramids and cones.

8. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Vocabulary slant height regular pyramid right cone

9. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones The slant height of a pyramid or cone is measured along its lateral surface. In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base. The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent. Right cone Regular Pyramid

10. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones

11. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Additional Example 1: Finding Surface Area Find the surface area of each figure B. S = r 2 + rl = 20.16 ft 2 = (3 2 ) + (3)(6) = 27  84.8 cm 2 A. S = B + Pl 1212 = (2.4 2.4) + (9.6)(3) 1212

12. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Try This 1: Finding Surface Area Find the surface area of each figure. = (3 3) + (12)(5) 1212 B. S = r 2 + rl = 39 m 2 = (7 2 ) + (7)(18) = 175  549.5 ft 2 5 m 3 m 7 ft 18 ft A. S = B + Pl 1212

13. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Additional Example 2: Exploring the Effects of Changing Dimensions A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.

14. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Try This: Example 2 Original DimensionsTriple the Slant Height Triple the Radius S = r 2 + rl = (4.5) 2 + (4.5)(2) = 29.25in 2  91.8 in 2 S = r 2 + r(3l) = (4.5) 2 + (4.5)(6) = 47.25in 2  148.4 in 2 S = r) 2 + r)l = (13.5) 2 + (13.5)(2) = 209.25in 2  657.0 in 2 A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

15. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Additional Example 3: Application The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass? = (10)(27.9)  876.1 mm 2 Pythagorean Theorem Lateral surface area L = rl a 2 + b 2 = l 2 10 2 + 26 2 = l 2 l  27.9

16. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Try This: Example 3 A road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone? = (4)(12.65)  158.9 in 2 12 in. 4 in. Pythagorean Theorem a 2 + b 2 = l 2 4 2 + 12 2 = l 2 l  12.65 Lateral surface area L = rl

17. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones PICK UP THE TRASH AROUND YOUR DESK! Thank you!

18. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones Lesson Quiz: Part 1 Find the surface area of each figure to the nearest tenth. Use 3.14 for . 1. the triangular pyramid 2. the cone 175.8 in 2 6.2 m 2

19. Pre-Algebra 6-9 Surface and Area of Pyramids and Cones 3. Tell whether doubling the dimensions of a cone will double the surface area. Lesson Quiz: Part 2 Insert Lesson Title Here It will more than double the surface area because you square the radius to find the area of the base.