Learn to find the volume of cones .

6-7 Volume of Pyramids and Cones Course 3 Essential Question Explain how the formula for the volume of cones is related to the formula for the volume of cylinders. Learn to find the volume of cones. Objective 8.G.9 (note that pyramids were removed from 8th grade; however, students need to be able to identify)

6-7 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Vocabulary pyramid cone (left next slide in for relevance on pyramids…amazing task so many years ago…)

6-7 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here The Great Pyramid of Giza http://www.gizapyramid.com/newtour1.htm The Great Pyramid is thought, by traditional scholars, to have been erected around 2600 BC during the reign of Khufu (whom the Greeks called Cheops) of the 4th Egyptian Dynasty. The great pyramid of Giza was built ~ 2.5 million years ago. Each block weighs ~ 2 tons and there is a belief that it took 20,000-30,000 people to build the pyramid!

6-7 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here NEVER use the slant as height! NOTE: another name for height is altitude! A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from thehighest point to the base along a perpendicular line.

6-7 Volume of Pyramids and Cones VOLUME OF PYRAMIDS AND CONES (22) Course 3

6-7 Volume of Pyramids and Cones 1 3 1 3 V = Bh V = • 9 • 10 Course 3 Additional Example 1B: Finding the Volume of Pyramids and Cones Find the volume of the figure. B. B = (32) = 9 in2 V = 30 94.2 in3 Use 3.14 for . Note: base is a circle

6-7 Volume of Pyramids and Cones 1 3 1 3 V = Bh V = • 9 • 7 Course 3 Try This: Example 1B Find the volume of the figure. B. B = (32) = 9 m2 7 m 3 m V = 21 65.9 m3 Use 3.14 for .

6-7 Volume of Pyramids and Cones Course 3 Additional Example 2: Exploring the Effects of Changing Dimensions A cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius. When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume.

6-7 Volume of Pyramids and Cones Original Dimensions Double the Height Double the Radius 1 3 V = pr2 (2h) V = pr2h V = p (2r)2h 1 3 1 3 1 3 = p(2 • 2)2(5) = p(22)(2•5) = p(22)5 1 3 1 3  20.93 m3  41.87 m3  83.73 m3 Course 3 Insert Lesson Title Here Try This: Example 2 A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius. When the height of a cone is doubled, the volume is doubled. When the radius is doubled, the volume is 4 times the original volume.

6-7 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Summary Volume of Cylinders & Cones are related… What relationship do you see between the 2?

6-7 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Lesson Quiz: Find the volume of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 6.3 m3 2. the cone 78.5 in3

Learn to find the volume of cones .