1. Bell Work: Find the total surface area of this figure. Use 3.14 for π. 6 cm 10 cm

2. Answer: 345.4 cm squared

3. LESSON 86: VOLUME OF PYRAMIDS AND CONES

4. We know how to compute the volume of cylinders and prisms. 4 cm 9 cm 10 in. 8 in. 6 in. Volume = B x h V = π(4cm) x 9cm V = (6 in. x 8 in.) x 10 in. V = 144π cm V = 480 in. 2 3 3

5. In this lesson we will learn the formulas to calculate the volumes of cones and pyramids, beginning with the formula for the volume of a cone.

6. Suppose we have a cone shaped container and a cylindrical can with the same diameters and heights.

7. To fill the can with water using the cone, we would have to fill and empty the cone three times.

8. The volume of a cone is 1/3 the volume of a cylinder with the same base diameter and height.

9. Example: Aidan built two cones out of sand on the beach. The diameter of the smaller cone is 6 in. and its height is 5 in. The diameter of the larger cone is 12 in. and its height is 10 in. How many cubic inches of sand did Aidan use for each cone? How many times greater is the volume of the larger cone than the volume of the smaller cone? Leave in terms of π.

10. Answer: Smaller Cone = 1/3π(3) (5) = 15π in. Larger Cone = 1/3π(6) (10) = 120πin. The larger cone has a volume 8 tines as large as the smaller cone. 3

11. The volume of prisms and pyramids are similarly related. From a block of clay in the shape of a prism, we can form 3 pyramids with the same base and height as the original prism.

12. The volume of a pyramid is 1/3 the volume of a prism with the same base and height.

13. Example: Find the volume of a square pyramid with a height of 50 cm and a base with a length of 90 cm and a width of 90 cm.

14. Answer: V = 1/3(90 cm) (50 cm) V = 135,000 cm 2 3

15. Example: A triangular pyramid is shown. The area of its base is 36√3 units. Its height is 10 units. What is its volume?

16. Answer: V = 1/3(36√3) x 10 V = 120√3 units cubed

17. HW: Lesson 86 #1-25