Videos, solutions, examples, and lessons to help Grade 8 students learn the formulas for the volumes of cones, cylinders, and
spheres and use them to solve real-world and mathematical problems.

Common Core: 8.G.9

### Suggested Learning Targets

Related Topics:

Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

**8.G.9 - Solid Geometry**

How to remember the formulas of a cylinder, a cone and a sphere?

Volume of cylinder = πr^{2}h

Volume of cone = 1/3 πr^{2}h

Volume of sphere = 4/3 πr^{3}

**Common Core in the Classroom: Finding the Volume of Cylinders, Cones, and Spheres**

Activities in the classroom to help you remember the formulas for cylinder, cone and sphere.**Cylindrical Volume 8.G.9**

In this common core example, we look at the volume of a cylinder and how the volume changes with changing dimensions.

Example:

If you have a cylinder with a height of 6 inches and a radius of 4 inches, what is the volume of the container. If we make the container 2 inches shorter and decrease the radius by 1 inch less, what is the new volume. How much larger is the original container?

**Volume of a Cone 8.G.9**

In this common core example, we construct and examine how to approximate the volume of a cone.

Example:

A sand pile in the shape of a cone is 8 feet tall with a diameter of 22 feet. Approximately how many cubic feet of sand are in the pile?**Volume, pi and Estimation 8.G.9**

How to find the empty space between the cylinder and the contents inside?

Example:

Three tennis balls with a diameter of 2.5 inches are placed inside a cylindrical container with a diameter of 2.7 inches and a height of 8.5 inches. Approximately, how much empty space is inside the container?**Comparing spheres, cones, and cylinders**

In this problem, we compare the volumes of a sphere, cone and cylinder of equal radius

Common Core: 8.G.9

- I can identify and define vocabulary: cone, cylinder, sphere, radius, diameter,

circumference, area, volume, pi, base, height - I can recognize formulas for volume of cones, cylinders, and spheres.
- I can compare the volume of cones, cylinders, and spheres
- I can determine and apply appropriate volume formulas in order to solve

mathematical and real-world problems for the given shape - I can, given the volume of a cone, cylinder, or sphere, find the radii, height, or

approximate for pi.

Related Topics:

Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

How to remember the formulas of a cylinder, a cone and a sphere?

Volume of cylinder = πr

Volume of cone = 1/3 πr

Volume of sphere = 4/3 πr

Activities in the classroom to help you remember the formulas for cylinder, cone and sphere.

In this common core example, we look at the volume of a cylinder and how the volume changes with changing dimensions.

Example:

If you have a cylinder with a height of 6 inches and a radius of 4 inches, what is the volume of the container. If we make the container 2 inches shorter and decrease the radius by 1 inch less, what is the new volume. How much larger is the original container?

In this common core example, we construct and examine how to approximate the volume of a cone.

Example:

A sand pile in the shape of a cone is 8 feet tall with a diameter of 22 feet. Approximately how many cubic feet of sand are in the pile?

How to find the empty space between the cylinder and the contents inside?

Example:

Three tennis balls with a diameter of 2.5 inches are placed inside a cylindrical container with a diameter of 2.7 inches and a height of 8.5 inches. Approximately, how much empty space is inside the container?

In this problem, we compare the volumes of a sphere, cone and cylinder of equal radius

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