Back To Course

CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Log in here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, we'll look at what makes cubes unique among three-dimensional shapes, and we'll put that uniqueness to use in finding an easy way to find the surface area of cubes.

Before we determine the surface area of a cube, let's determine exactly what surface area is.

For a two-dimensional shape, the **area** is the space that it covers. Think about calculating the number of tiles needed for a floor or the amount of space inside a rectangular fence. We have formulas to calculate the areas of different shapes, like squares, triangles, and circles.

But what about three-dimensional shapes? Since they're three-dimensional, they have an outside, or surface. **Surface area** is just what it sounds like - the area of the shape's surface, which is its entire outside. Think about determining the amount of paint needed to cover a house or the total surface space of a box. Just like there are different ways to find the areas of different two-dimensional shapes, there are also ways to find the surface areas of different three-dimensional shapes like cubes, pyramids, and spheres.

Let's look at how to find the surface area of a cube.

**Cubes** are three-dimensional shapes that have the same dimensions all over. The length, width, and height are identical, and every edge meets every other edge at the same angle. They are highly regular!

Finding the surface area of a cube is nice and convenient because by definition its surface consists of **congruent**, or equal-sized, squares. So, once we find the area of one of the squares, we know the area of all of the squares. But how many squares are there?

From this illustration of a cube, we can see that it has a front and a back, two sides, a top, and bottom. So the cube's surface consists of **six congruent squares**. In fact, if we unfold the cube, we can clearly see the six squares that make up its surface.

All we really need is the length of a side of one of these squares, which would also be one edge of the cube. Let's say that the cube's height is two inches. Because the cube's surface is made of squares, all of its edges will be the same length. So if the cube's height is two inches, its length and width will also be two inches.

To find the area of one of the squares, we go back to basic geometry and recall that Area (A) = s^2, where s is the length of one of the sides. In this case, *s* = 2 inches, so A = 2 in^2 = 2 in * 2 in = 4 in^2.

The area of one of the surface squares is four square inches.

Since the entire surface consists of six congruent squares, we just have to multiply the area of that single square by six to find the total surface area. So:

4 in^2 * 6 = 24 in^2

The cube's surface area is 24 square inches.

Now that we've determined that the surface area of a cube is six times the area of one of its surface squares, we can say that the equation for a cube's surface area is:

A = 6 * *s* * *s* or 6*s*^2

Let's apply this to a bigger cube that's ten feet wide.

As we've discovered, if the cube is ten feet wide, it's also ten feet high, so we can find the area of one of these squares:

A = 10 ft * 10 ft = 100 ft^2

The area of one square is 100 square feet.

To find the entire surface area, we need to take into account all six squares that make up the cube's surface:

100 ft^2 * 6 = 600 ft^2

This cube's surface area is 600 square feet. The method works the same way no matter how small or large the cube is.

A cube's surface is made up of **six congruent squares**, so we can follow a simple formula to find any cube's surface area. Since the area of one square with length *s* is *s* times *s*, to find the entire surface area of any cube, we can just multiply that by 6. Our formula for the surface area of a cube, then, is:

Surface Area = 6 * *s* * *s* = 6*s*^2

The only number we need to know to find a cube's surface area is the length of one of its edges! Cubes are fairly simple after all.

**area**: the space that a two-dimensional shape covers**surface area**: the space that a three-dimensional shape covers; the entire outside of a three-dimensional shape- Surface Area of a Cube = 6 *
*s***s*= 6*s*^2

- Surface Area of a Cube = 6 *
**cube**: three-dimensional shape that has identical length, width, and height; consists of six congruent squares**congruent**: equal-sized

After reading about the surface area of cubes, you should be able to

- Contrast between area and surface area.
- Describe the shape of a cube.
- Calculate the surface area of a cube.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
13 in chapter 18 of the course:

Back To Course

CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

- Perimeter of Triangles and Rectangles 8:54
- Area of Triangles and Rectangles 5:43
- Circles: Area and Circumference 8:21
- Volume of Cylinders, Cones, and Spheres 7:50
- Volume of Prisms and Pyramids 6:15
- How to Find Surface Area of a Cube and a Rectangular Prism 4:08
- How to Find Surface Area of a Cylinder 4:26
- How to Find Surface Area of a Pyramid 5:11
- Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures 7:33
- Area Method: Slope & Examples
- Finding the Area of a Cylinder: Formula & Example 3:06
- How to Calculate the Volume of a Cube: Formula & Practice 5:16
- How to Find the Surface Area of a Cube 4:35
- Go to CAHSEE - Perimeter, Area & Volume in Geometry: Help and Review

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What is Deadlock? - Definition, Examples & Avoidance
- El Hombre que se Convirtio en Perro: Author, Summary & Theme
- Achilles in The Iliad: Character Analysis & Description
- A Wrinkle in Time Chapter 5 Summary
- Roald Dahl Project Ideas
- Media Literacy Activities for High School
- Letter M Activities
- Quiz & Worksheet - Shang Dynasty Religion & Culture
- Quiz & Worksheet - Alternative Assessment Types
- Quiz & Worksheet - Population Composition
- Quiz & Worksheet - Minimalist Painters
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- 6th Grade Math Worksheets & Printables
- Elementary School Math Worksheets & Printables

- SAT Subject Test World History: Practice and Study Guide
- Music 101: Intro to Music
- 9th Grade English Curriculum Resource & Lesson Plans
- Macroeconomics Syllabus Resource & Lesson Plans
- NES Middle Grades General Science (204): Practice & Study Guide
- The High Middle Ages: Homeschool Curriculum
- GRE Analytical Writing - Crafting Your Argument: Help and Review
- Quiz & Worksheet - Crystals: Types & Properties
- Quiz & Worksheet - Long Division
- Quiz & Worksheet - Autopsy Procedure & Results
- Quiz & Worksheet - Characteristics of Short Stories
- Quiz & Worksheet - Price Floor in Economics

- Frost Wedging: Definition & Example
- Joseph Lister: Biography, Facts & Inventions
- How to View Grades and Export CSVs in Your Study.com Virtual Classroom
- Found Poetry Lesson Plan
- Next Generation Science Standards in Massachusetts
- And Then There Were None Lesson Plan
- Homeschooling in Ohio
- Cool Science Facts
- Bristol, CT Adult Education
- Sustainability Project Ideas
- What is a Distance Learning Course?
- How to Ace the LSAT

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject