Simple examples: How a cube and a rectangular prism are alike

📚 Quick Study Guide

• 🧊 Definition of a Cube: A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. All sides are of equal length.
• 🧱 Definition of a Rectangular Prism: A rectangular prism is a three-dimensional solid object which has six faces that are rectangles.
• 📐 Faces, Edges, and Vertices: Both cubes and rectangular prisms have 6 faces, 12 edges, and 8 vertices.
• ✨ Similarities: Both are polyhedra, meaning they are 3D shapes with flat faces. Both are also prisms because they have two parallel faces (bases) that are congruent polygons.
• ➕ Key Difference: The main difference is that all faces of a cube are squares, while a rectangular prism has faces that are rectangles (which can include squares). So, a cube is a special type of rectangular prism.
• 📏 Volume Formula (Rectangular Prism): Volume, $V = l \times w \times h$, where $l$ is length, $w$ is width, and $h$ is height.
• ➗ Volume Formula (Cube): Since all sides are equal, Volume, $V = s^3$, where $s$ is the side length.

Practice Quiz

1. Which of the following characteristics do both cubes and rectangular prisms share?

   1. They both have 5 faces.
   2. They both have 6 faces.
   3. They both have circular faces.
   4. They both have 10 edges.

2. How many vertices does a rectangular prism have?

   1. 6
   2. 12
   3. 8
   4. 4

3. What is the main difference between a cube and a rectangular prism?

   1. A cube has square faces, while a rectangular prism has rectangular faces.
   2. A cube has rectangular faces, while a rectangular prism has square faces.
   3. A cube has 8 faces, while a rectangular prism has 6 faces.
   4. There is no difference between a cube and a rectangular prism.

4. A cube can also be classified as a:

   1. Sphere
   2. Rectangular Prism
   3. Cylinder
   4. Pyramid

5. What is the formula for the volume of a rectangular prism?

   1. $V = s^3$
   2. $V = l + w + h$
   3. $V = l \times w \times h$
   4. $V = 2lw + 2lh + 2wh$

6. How many edges does a cube have?

   1. 6
   2. 8
   3. 10
   4. 12

7. Which of the following is NOT a shared characteristic of cubes and rectangular prisms?

   1. Having 6 faces
   2. Having 8 vertices
   3. Having 12 edges
   4. Having all faces as squares