GEOMETRY Volume of Cylinders, Cones, Spheres 8 th Math Presented by Mr. Laws

Standard 8.G.9 – Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Essential Question Using math principles, what is the effect on the volume of a cylinder, cones, or sphere once the radius or height has change?

Definitions 3 Dimensional (3-D) – It is the length, width, and height of solid figures. Prisms – are 3-D figures that have two bases. Example: Cylinder. Pyramids 3-D figures that have one base. Example: Cones Hemi-sphere – is half of a sphere or round solid figure.

Volume of Solid Figures Volume is the amount of cubic units that can fit or into or fill a solid figure. All volume answers will be in Cubic Units! Example: 25 ft 3, 2560 m 3, etc…

Solid Figures Prisms have two bases such as a cylinder, cube, rectangular, and triangular prisms. Pyramids have one base, such as a square pyramid, triangular pyramid, and cone.

Part I : Finding the Volume of a Cylinder Radius (r) Height (h) r 2 = radius x radius V = volume h = height

Finding the Volume of a Cylinder? 5 m 10 m V = 785 m 3 Use 3.14 for pi Note: If you use calculator pi, it will give you a more accurate decimal answer. Example # 1

Finding the Volume of a Cylinder? 7 yds 12 yds V = yd 3 Use 3.14 for pi What do you notice about using the formula this time? Example # 2

Part I SUMMARY What are some key concepts you should remember about finding the volume of a cylinder Is there more you need to learn about this concept? Can you answer the essential question or do you have any more questions concerning this lesson?

Part II: Finding the Volume of a Cone Finding the volume of a cone uses the same formula as finding the volume of cylinder except it is divided by 1/3 (one-third).

Finding the Volume of a Cone V = m 3 Use 3.14 for pi Example # 3

Finding the Volume of a Cone V = in 3 4 in. 8.6 in Example # 4 Use 3.14 for pi

Part II SUMMARY What are some key concepts you should remember about finding the volume of a cone. Is there more you need to learn about this concept? Can you answer the essential question or do you have any more questions concerning this lesson?

Part III: Finding the Volume of a Sphere Finding the volume of a sphere is equal to 4 times pi times radius cube, divided by three.

Finding the Volume of a Sphere V = cm 3 Use 3.14 for pi Example # 5

Finding the Volume of a Sphere V = m 3 Use 3.14 for pi Example # 6

Part III SUMMARY What are some key concepts you should remember about finding the volume of a Sphere. Is there more you need to learn about this concept? Can you answer the essential question or do you have any more questions concerning this lesson?