In mathematics, a cube is a three-dimensional shape with six square faces, twelve edges, and eight vertices. Each face of a cube is a square, and all the edges of a cube are of equal length. The cube is a special case of a rectangular prism, where all the sides are of equal length.

Here are some important formulas and properties related to a cube:

**Volume of a Cube:**The volume (V) of a cube with side length (a) is given by the formula: V = a^{3}.**Surface Area of a Cube:**The total surface area (A) of a cube with side length (a) is given by the formula: A = 6a^{2}.**Diagonal of a Cube:**The length of the diagonal (d) of a cube with side length (a) is given by the formula: d = a√3.

Here's a study guide to help you understand and work with cubes:

- Understand the definition and properties of a cube.
- Learn the formulas for calculating the volume, surface area, and diagonal of a cube.
- Practice solving problems related to cubes, such as finding the volume or surface area given the side length.
- Understand the relationship between the side length, volume, and surface area of a cube.
- Explore real-life examples and applications of cubes, such as finding the volume of a cube-shaped box.

By mastering the concepts and properties of cubes, you'll be well-prepared to apply this knowledge to various mathematical problems and real-world scenarios.

.Study GuideGeometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key Numerical & Geometric Proportions

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.