Calculate Cube Volume: Finding Volume When Edge Length is 7 cm

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

A cube is three-dimensional, so we need length × width × height. Since all edges are equal (7 cm), we multiply 7 × 7 × 7 = 7³. Multiplying by 3 would only give us the perimeter of one face!

Q: What's the difference between cm² and cm³?

cm² measures area (like the face of the cube), while cm³ measures volume (the space inside). Volume always uses cubic units because we're measuring 3D space!

Q: How can I remember that 7³ = 343?

Break it down step by step: 7 × 7 = 49, then 49 × 7 = 343. You can also think of it as building 7 layers of 7×7 squares!

Q: What if the edge length was a decimal, like 7.5 cm?

The same formula applies! You'd calculate $ 7.5^3 = 7.5 \times 7.5 \times 7.5 $. Just be extra careful with your decimal multiplication.

Q: Can I use a calculator for this?

Absolutely! For $ 7^3 $, you can enter 7 × 7 × 7 or use the exponent key. Just make sure to double-check your answer makes sense.

Cube Volume with Integer Edge Length

The edges of a cube are 7 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

00:05 Let's calculate the volume of the cube.

00:08 First, check the edge length from the data.

00:12 We'll use the formula: edge length, to the power of three.

00:17 Now, substitute the edge length and find the volume.

00:21 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The edges of a cube are 7 cm long.

Calculate the volume of the cube.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: Identify the given information.
The length of each edge of the cube is given as $7$ cm.

Step 2: Apply the appropriate formula.
The formula for the volume $V$ of a cube where each edge is of length $s$ is given by $V = s^3$ .

Step 3: Perform the necessary calculations.
Plugging in the value of $s = 7$ cm, we compute the volume as follows:
$V = 7^3 = 7 \times 7 \times 7 = 343 \text{ cm}^3$

Therefore, the volume of the cube is $343$ cm³.

Final Answer

$343$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: V = s³
Calculation: With edge 7 cm: V = 7³ = 7 × 7 × 7 = 343
Check: Units are cubic centimeters (cm³) and 7 × 7 = 49, then 49 × 7 = 343 ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or calculating incorrectly
Don't use V = 7 × 6 = 42 or V = 7² = 49! These give surface area formulas or wrong powers. The volume formula requires cubing (multiplying three times), so always use V = s³ = s × s × s.

Practice Quiz

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FAQ

Everything you need to know about this question

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

A cube is three-dimensional, so we need length × width × height. Since all edges are equal (7 cm), we multiply 7 × 7 × 7 = 7³. Multiplying by 3 would only give us the perimeter of one face!

What's the difference between cm² and cm³?

cm² measures area (like the face of the cube), while cm³ measures volume (the space inside). Volume always uses cubic units because we're measuring 3D space!

How can I remember that 7³ = 343?

Break it down step by step: 7 × 7 = 49, then 49 × 7 = 343. You can also think of it as building 7 layers of 7×7 squares!

What if the edge length was a decimal, like 7.5 cm?

The same formula applies! You'd calculate $7.5^3 = 7.5 \times 7.5 \times 7.5$ . Just be extra careful with your decimal multiplication.

Can I use a calculator for this?

Absolutely! For $7^3$ , you can enter 7 × 7 × 7 or use the exponent key. Just make sure to double-check your answer makes sense.

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