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,

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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.

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.

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.

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 Volume of Pyramids, Cones, and Spheres

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 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

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 Volume of Pyramids, Cones, and Spheres 5 ft 6 ft 3 ft Multiply.

Additional Example 1B: Finding the Volume of the Pyramid Find the volume of the pyramid. Course 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 ·

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 Volume of Pyramids, Cones, and Spheres 9 ft 7 ft 4 ft Multiply.

Try This: Example 1B Find the volume of the pyramid. Course 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 · h = 8 m 3 m h = 4 m

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 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

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 yd 3. Use the formula. Substitute. Multiply. Course Volume of Pyramids, Cones, and Spheres

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  The volume is about 12.6 yd 3. Use the formula. Substitute. Multiply. Course Volume of Pyramids, Cones, and Spheres Try This: Example 2 3 yd 2 yd

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.

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.