Calculate Cube Volume and Area: 8 cm Edge Length Problem

Q: Why is the volume formula $ a^3 $ and not $ 3a $ ?

Volume measures 3-dimensional space inside the cube. You need length × width × height, and since all edges equal 8 cm, that's $ 8 × 8 × 8 = 8^3 = 512 $ cubic cm!

Q: Where does the 6 come from in the surface area formula?

A cube has 6 faces: top, bottom, front, back, left, and right. Each face is a square with area $ a^2 $, so total surface area is $ 6 × a^2 $.

Q: What's the difference between $ cm^2 $ and $ cm^3 $ ?

$ cm^2 $ measures area (like covering the cube's surface with paint), while $ cm^3 $ measures volume (like filling the cube with water). Always match your units to what you're calculating!

Q: Can I just memorize that 8 cubed equals 512?

Understanding is better than memorizing! Know that $ 8^3 = 8 × 8 × 8 $. First calculate $ 8 × 8 = 64 $, then $ 64 × 8 = 512 $. This method works for any edge length.

Q: How do I remember which formula to use?

Think about what you're measuring! Volume = space inside (3D) = $ a^3 $. Surface area = covering the outside (2D faces) = $ 6a^2 $. The number of dimensions in the answer tells you which formula to use.

Cube Volume and Surface Area with Standard Formulas

The length of each edge in the cube is 8 cm.

Calculate the volume and area of the cube.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the volume and surface area of the cube

00:03 We'll use the formula to calculate the cube's volume (edge length cubed)

00:07 We'll substitute appropriate values and solve for the volume

00:23 This is the cube's volume, now let's calculate its surface area

00:27 We'll use the formula to calculate the surface area of the cube

00:31 We'll substitute appropriate values and solve for the surface area

00:41 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The length of each edge in the cube is 8 cm.

Calculate the volume and area of the cube.

Step-by-step solution

To solve this problem, we will calculate the volume and surface area of a cube with edge length 8 cm.

Step 1: Calculate the volume of the cube using the formula $V = a^3$ .

Given that the edge length $a = 8$ cm, the volume is calculated as follows:

$V = 8^3 = 8 \times 8 \times 8 = 512 \text{ cm}^3$

Step 2: Calculate the surface area of the cube using the formula $S = 6a^2$ .

Using the same edge length $a = 8$ cm, we find the surface area:

$S = 6 \times 8^2 = 6 \times (8 \times 8) = 6 \times 64 = 384 \text{ cm}^2$

Thus, the calculated volume and surface area of the cube are, respectively, 512 cm $^3$ and 384 cm $^2$ .

Therefore, the correct solution to the problem, matching the given answer choices, is choice 1: $V = 512, S = 384$ .

Final Answer

$V=512,S=384$

Key Points to Remember

Essential concepts to master this topic

Volume Formula: Cube volume equals edge length cubed: $V = a^3$
Surface Area: Six square faces give $S = 6a^2$ total area
Check: Volume units are cubic, surface area units are square ✓

Common Mistakes

Avoid these frequent errors

Confusing volume and surface area formulas
Don't use $V = 6a^2$ for volume = 384 instead of 512! Surface area uses 6 faces, but volume needs all 3 dimensions multiplied. Always remember: volume is $a^3$ , surface area is $6a^2$ .

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

Why is the volume formula $a^3$ and not $3a$ ?

Volume measures 3-dimensional space inside the cube. You need length × width × height, and since all edges equal 8 cm, that's $8 × 8 × 8 = 8^3 = 512$ cubic cm!

Where does the 6 come from in the surface area formula?

A cube has 6 faces: top, bottom, front, back, left, and right. Each face is a square with area $a^2$ , so total surface area is $6 × a^2$ .

What's the difference between $cm^2$ and $cm^3$ ?

$cm^2$ measures area (like covering the cube's surface with paint), while $cm^3$ measures volume (like filling the cube with water). Always match your units to what you're calculating!

Can I just memorize that 8 cubed equals 512?

Understanding is better than memorizing! Know that $8^3 = 8 × 8 × 8$ . First calculate $8 × 8 = 64$ , then $64 × 8 = 512$ . This method works for any edge length.

How do I remember which formula to use?

Think about what you're measuring! Volume = space inside (3D) = $a^3$ . Surface area = covering the outside (2D faces) = $6a^2$ . The number of dimensions in the answer tells you which formula to use.

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Calculate Cube Volume and Area: 8 cm Edge Length Problem

Cube Volume and Surface Area with Standard Formulas

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the volume formula $a^3$ and not $3a$ ?

Where does the 6 come from in the surface area formula?

What's the difference between $cm^2$ and $cm^3$ ?

Can I just memorize that 8 cubed equals 512?

How do I remember which formula to use?

🌟 Unlock Your Math Potential

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❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the volume formula a3 a^3 a3 and not 3a 3a 3a?

Where does the 6 come from in the surface area formula?

What's the difference between cm2 cm^2 cm2 and cm3 cm^3 cm3?

Can I just memorize that 8 cubed equals 512?

How do I remember which formula to use?

🌟 Unlock Your Math Potential

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