1. 04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Warm-Up LT: I will calculate the volume of prisms, cylinders, pyramids, and cones. Start working on the volume side of the pink worksheet. Show your formula, substitution, and answer for each problem.

2. 04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Problem Solving Page LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.

3. 04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Predict: 1.Looking at a pyramid and prism that share the same size base and height, how much smaller is the pyramid’s volume? 2. Looking at a cone and cylinder that share the same size base and height, how much smaller is the cone’s volume? LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.

4. If you pour sand from a pyramid-shaped container into a prism-shaped container with the same height, base shape, and base size, you will discover an interesting relationship. The prism-shaped container holds three times as much sand as the pyramid-shaped container. Course 2 9-3 Volume of Pyramids, Cones, and Spheres

5. In fact, the volume of a pyramid is exactly one- third the volume of a prism that has the same height, base shape, and base size as the pyramid. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex. Course 2 9-3 Volume of Pyramids, Cones, and Spheres VOLUME OF A PYRAMID The volume V of a pyramid is one-third the area of its base B times its height h. V = Bh 1 3

6. Find the volume of the pyramid. Additional Example 1A: Finding the Volume of a Pyramid A. V = 1313 Bh Use the formula. B = 5 · 6 = 30 Find the area of the rectangular base. V = 1313 · 30 · 3 Substitute for B and h. V = 30 The volume is 30 ft 3. Course 2 9-3 Volume of Pyramids, Cones, and Spheres 5 ft 6 ft 3 ft Multiply.

7. Additional Example 1B: Finding the Volume of the Pyramid Find the volume of the pyramid. Course 2 9-3 Volume of Pyramids, Cones, and Spheres B. V = 1313 Bh Use the formula. B = 2 · 3 = 3 Find the area of the triangular base. V = 1313 · 3 · 5 V = 5 The volume is 5 cm 3. Multiply. Substitute for B and h. 1212 ·

8. Find the volume of the pyramid. Try This: Example 1A A. V = 1313 Bh Use the formula. B = 9 · 7 = 63 Find the area of the rectangular base. V = 1313 · 63 · 4 Substitute for B and h. V = 84 The volume is 84 ft 3. Course 2 9-3 Volume of Pyramids, Cones, and Spheres 9 ft 7 ft 4 ft Multiply.

9. Try This: Example 1B Find the volume of the pyramid. Course 2 9-3 Volume of Pyramids, Cones, and Spheres B. V = 1313 Bh Use the formula. B = 3 · 8 = 12 Find the area of the triangular base. V = 1313 · 12 · 4 V = 16 The volume is 16 m 3. Multiply. Substitute for B and h. 1212 · h = 8 m 3 m h = 4 m

10. The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base. The height of a cone is the perpendicular distance from the cone’s base to its vertex. Course 2 9-3 Volume of Pyramids, Cones, and Spheres VOLUME OF A CONE The volume V of a cone is one-third the area of its base, r 2, times its height h. V = r 2 h 1 3

11. Find the volume of a cone to the nearest tenth. Use 3.14 for . Additional Example 2: Finding the Volume of a Cone V = 1313 r2hr2h V  1313 · 3.14 · 5 2 · 6 V  157 The volume is about 157.0 yd 3. Use the formula. Substitute. Multiply. Course 2 9-3 Volume of Pyramids, Cones, and Spheres

12. Find the volume of a cone to the nearest tenth. Use 3.14 for . V = 1313 r2hr2h V  1313 · 3.14 · 2 2 · 3 V  12.56 The volume is about 12.6 yd 3. Use the formula. Substitute. Multiply. Course 2 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 2 3 yd 2 yd

13. 04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Period 1: Page 482 #1-6 For each problem show the formula, substitution, and answer with units. LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.

14. 04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Period 5: Finish both sides of worksheet for homework. For each problem show the formula, substitution, and answer with units. LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.