Calculate Cube Volume: Finding V = s³ for a 5cm Edge

Q: Why do I cube the edge length instead of just multiplying by 3?

A cube has three dimensions - length, width, and height. Since all edges are equal (5 cm each), you multiply 5 × 5 × 5 to find how many cubic centimeters fit inside the cube.

Q: What does the ³ symbol in cm³ mean?

The ³ (cubed) shows that volume measures three-dimensional space. It means cubic units - like stacking small 1cm × 1cm × 1cm blocks to fill the entire cube.

Q: How is this different from finding the area of a square?

Area uses $ A = s^2 $ for flat surfaces (like square cm). Volume uses $ V = s^3 $ for space inside 3D objects (like cubic cm).

Q: Can I use this formula for any cube size?

Yes! Whether the edge is 2 cm, 10 cm, or even 0.5 cm, always use $ V = a^3 $. Just substitute your edge length for a and cube it.

Q: What if I forget how to calculate 5³?

Break it down: $ 5^3 = 5 \times 5 \times 5 $. First find 5 × 5 = 25, then multiply 25 × 5 = 125. Always work step by step!

Volume Calculation with Cubic Units

A cube has edges measuring 5 cm long.

Calculate the volume 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 of the cube

00:03 We'll use the formula for calculating cube volume (edge to the third power)

00:07 We'll substitute the edge value according to the given data and solve for the volume

00:13 We'll break down a number to the third power into multiplying it by itself 3 times

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A cube has edges measuring 5 cm long.

Calculate the volume of the cube.

Step-by-step solution

To solve this problem, we'll calculate the volume of the cube using the formula for the volume of a cube, which is $V = a^3$ , where $a$ is the length of an edge.

Step-by-step solution:

Step 1: Identify the given length of the cube's edge. Here, $a = 5$ cm.
Step 2: Apply the formula for the volume of a cube: $V = a^3$ .
Step 3: Substitute the value of $a$ into the formula: $V = 5^3$ .
Step 4: Calculate $5^3$ . Since $5 \times 5 = 25$ and $25 \times 5 = 125$ , we get $5^3 = 125$ .

Therefore, the volume of the cube is $125$ cm $^3$ .

Looking at the answer choices, the correct answer is choice 2: $125$ cm $^3$ .

Final Answer

$125$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = a^3$
Technique: Calculate $5^3 = 5 \times 5 \times 5 = 125$ step by step
Check: Units must be cubic (cm³) and answer makes sense for a 5cm cube ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or forgetting to cube
Don't calculate $5 \times 6 = 30$ or $5^2 = 25$ for volume = wrong units and wrong answer! Volume needs all three dimensions multiplied together. Always use $V = a^3$ and multiply the edge length three times.

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 do I cube the edge length instead of just multiplying by 3?

A cube has three dimensions - length, width, and height. Since all edges are equal (5 cm each), you multiply 5 × 5 × 5 to find how many cubic centimeters fit inside the cube.

What does the ³ symbol in cm³ mean?

The ³ (cubed) shows that volume measures three-dimensional space. It means cubic units - like stacking small 1cm × 1cm × 1cm blocks to fill the entire cube.

How is this different from finding the area of a square?

Area uses $A = s^2$ for flat surfaces (like square cm). Volume uses $V = s^3$ for space inside 3D objects (like cubic cm).

Can I use this formula for any cube size?

Yes! Whether the edge is 2 cm, 10 cm, or even 0.5 cm, always use $V = a^3$ . Just substitute your edge length for a and cube it.

What if I forget how to calculate 5³?

Break it down: $5^3 = 5 \times 5 \times 5$ . First find 5 × 5 = 25, then multiply 25 × 5 = 125. Always work step by step!

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