Volume Study Guide
What is Volume?
Volume is the amount of space occupied by a three-dimensional object. It is measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3).
Formulas for Calculating Volume
There are different formulas for calculating the volume of different shapes:
- Cube: Volume = s3, where s is the length of a side.
- Rectangular Prism: Volume = length × width × height.
- Cylinder: Volume = πr2h, where r is the radius of the base and h is the height.
- Sphere: Volume = (4/3)πr3, where r is the radius.
- Cone: Volume = (1/3)πr2h, where r is the radius of the base and h is the height.
Example Problems
Let's solve some example problems to practice calculating volumes.
Example 1: Cube
If the side length of a cube is 5 cm, what is its volume?
Volume = 53 = 125 cm3.
Example 2: Rectangular Prism
A rectangular prism has a length of 7 cm, a width of 4 cm, and a height of 3 cm. What is its volume?
Volume = 7 × 4 × 3 = 84 cm3.
Example 3: Cylinder
If the radius of a cylinder is 2 m and the height is 6 m, what is its volume?
Volume = π × 22 × 6 = 24π m3.
Study Tips
Here are some tips for studying volume:
- Practice using the volume formulas for different shapes.
- Understand the concept of volume as the amount of space occupied by an object.
- Work on visualizing the shapes and how they occupy space in three dimensions.
- Review and memorize the formulas for calculating volume.
- Solve plenty of practice problems to reinforce your understanding.
[Volume] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Eighth Grade. Plane figures
Study Guide
Plane figures 
Worksheet/Answer key
Plane figures Worksheet/Answer key
Plane figures Worksheet/Answer key
Plane figures Worksheet/Answer key
Plane Geometry
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Geometry (NCTM)
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
Use coordinate geometry to represent and examine the properties of geometric shapes.
Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.