High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
Here you will learn about the surface area of a cube, including how to calculate the surface area of a cube and how to find missing values of a cube given its surface area.
Students will first learn about the surface area of a cube as a part of geometry in 8 th grade.
The surface area of a cube (cuboid) is the sum of the areas of all the faces of a cube. This is also referred to as the total surface area of a cube (tsa) or the lateral surface area of a cube.
A cube is a three-dimensional figure that has six congruent square faces. This means that all the side faces are the same size.
To find the area of each face, multiply the side lengths together. Then multiply the area of each of the square faces by six.
The formula to calculate the surface area, S, of a cube is S=6x^{2} where x represents the side length (edge length) of the cube.
The surface area of a cube formula can be used to find the surface area of any cube.
Surface area is measured in square units, for example mm^{2}, \, cm^{2} or \, m^{2}.
How does this relate to 8 th grade math?
Use this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!
DOWNLOAD FREEIn order to calculate the surface area of a cube:
Find the surface area of the cube below.
2Substitute any known value(s) into the formula.
Here, x=5 and so S=6\times{5}^{2}.
3Complete the calculation.
S=6\times{5}^{2}=6\times{25}=1504Write the solution, including the units.
As the unit of length is centimeters (cm), the unit of area is square centimeters (cm^{2}).
S=150 \, cm^{2}Find the surface area of the cube.
Write the formula for the surface area of the cube.
Substitute any known value(s) into the formula.
Substituting x=6 into the formula, we have S=6\times{6}^{2}.
Complete the calculation.
Write the solution, including the units.
As the unit of length is centimeters (cm), the unit of area is square centimeters (cm^{2}).
S=216 \, cm^{2}
A cube structure has a side length of 7 \, m. Calculate the total surface area of the structure.
Write the formula for the surface area of the cube.
Substitute any known value(s) into the formula.
Substituting x=7 into the formula, S=6\times{7}^{2}.
Complete the calculation.
Write the solution, including the units.
As the unit of length is meters (m), the unit of area is square meters (m^{2}).
S=294 \, m^{2}
The area of the face of a cube is 30 \, cm^{2}. Find the surface area of the cube.
Write the formula for the surface area of the cube.
Substitute any known value(s) into the formula.
Knowing the area of one face of the cube, you can express this as x^2=30 as x is the side length of the cube, and you know the area, x^2.
Substituting x^2=30 into the formula, you have S=6\times{30}.
Complete the calculation.
Write the solution, including the units.
As the unit of area is square centimeters (cm^{2}), you can use this in the solution.
S=180 \, cm^{2}
The surface area of a cube is 24 \, ft^{2}. Find the length of the cube.
Write the formula for the surface area of the cube.
Substitute any known value(s) into the formula.
Here you know that S=24 and so substituting this into the formula,
24=6\times{x}^{2}.Complete the calculation.
To complete the calculation, divide both sides by 6 first, and then square root both sides to find x.
Write the solution, including the units.
As the unit of area is square feet (ft^2), the unit length will be in feet.
x=2 \, ft
The surface area of a cube is 483 \, mm^{2}. Find the length of the side x correct to 2 decimal places.
Write the formula for the surface area of the cube.
Substitute any known value(s) into the formula.
As you know the surface area, you can substitute S=483 into the formula 483=6\times{x}^{2}.
Complete the calculation.
To complete the calculation, divide both sides by 6 first, and then square root both sides to find x.
Write the solution, including the units.
1. Find the surface area of the cube.
S=6x^{2} where x=3 \, cm.
S=6\times{3}^{2}=6\times{9}=54 \, cm^{2}.
2. Calculate the surface area of the cube below. Write your answer in square centimeters.
S=6x^{2} where x=0.5 \mathrm{~m}=50 \mathrm{~cm}.
S=6\times{50}^{2}=6\times{2500}=15,000 \, cm^{2}.
3. Find the surface area of the cube. Give your answer in cm^2.
S=6x^{2} where x=40 \mathrm{~cm}=0.4 \mathrm{~m}.
S=6\times{40}^{2}=6\times{1600}=9,600 \, cm^{2}.
4. The surface area of a cube is 150 \, cm^2. Find the length of the side of the cube.
S=6x^{2} where S=150 \, cm^{2}.
\begin{aligned}150&=6\times{x}^{2} \\\\ 25&=x^{2} \\\\ x&=\sqrt{25} \\\\ x&=5cm \end{aligned}
5. The surface area of the cube is 6 \, m^2. Find the length of each side x.
S=6x^{2} where S=6 \, m^{2}.
\begin{aligned}6&=6\times{x}^{2} \\\\ 6\div{6}&=x^{2} \\\\ x^{2}&=1 \\\\ x&=\sqrt{1} \\\\ x&=1m \end{aligned}
6. The surface area of a cube is 186 \, m^2. Find the length of each side. Write your answer to the nearest centimeter.
S=6x^{2} where S=186 \, m^{2}.
\begin{aligned}186&=6\times{x}^{2} \\\\ 31&=x^{2} \\\\ x&=\sqrt{31}=5.567764362830…=5.57 \, (2 d p). \end{aligned}
A cube is a three-dimensional figure with six equal square faces and 8 vertices.
To find the volume of a cube, you will use the formula V=a^3 or
V=\text { side } \times \text { side } \times \text { side }.
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs.
Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!