GEOMETRY Volume of Cylinders Cones Spheres 8 th

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?

Target Statement Ø I CAN find the volume of a cylinder. Ø I CAN find the volume of a cone. Ø I CAN find the volume of a sphere.

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 • Sphere a 3 -D figure that is shape like a ball or globe. • 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 Formula: Radius (r) V = volume Height (h) r 2 = radius x radius h = height

Finding the Volume of a Cylinder? Example # 1 5 m Use 3. 14 for pi 10 m V = 785 m 3 Note: If you use calculator pi, it will give you a more accurate decimal answer.

Finding the Volume of a Cylinder? Example # 2 7 yds Use 3. 14 for pi What do you notice about this problem? 12 yds V = 461. 6 yd 3

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 Example # 3 Use 3. 14 for pi V = 1004. 8 m 3

Finding the Volume of a Cone Example # 4 8. 6 in 4 in. Use 3. 14 for pi V = 36. 006 in 3

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 Example # 5 Use 3. 14 for pi V = 4186. 6 cm 3

Finding the Volume of a Sphere Example # 6 Use 3. 14 for pi V = 11488. 2 m 3

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?