Finding Cube Edge Length: Converting 343 cm³ Volume to Side Length

Q: How do I find cube roots without a calculator?

Look for perfect cubes you know! Try small numbers: $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $, $ 4^3 = 64 $, $ 5^3 = 125 $, $ 6^3 = 216 $, $ 7^3 = 343 $.

Q: Why is the formula V = s³ and not V = 3s?

A cube has three dimensions all the same length. Volume is length × width × height, so $ s \times s \times s = s^3 $. The number 3 would only give you the perimeter of one face!

Q: How do I check if 343 is really 7³?

Multiply step by step: $ 7 \times 7 = 49 $, then $ 49 \times 7 = 343 $. You can also think of it as $ 7^2 \times 7 = 49 \times 7 = 343 $.

Q: Do all cubes have whole number edge lengths?

No! Only when the volume is a perfect cube (like 1, 8, 27, 64, 125, 216, 343...) will you get a whole number edge length. Most real cubes have decimal measurements.

Cube Root Operations with Perfect Cubes

A cube has a volume of 343 cm³.

How long are the cube's edges?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the cube's edge

00:03 We'll use the formula for calculating cube volume (edge to the power of 3)

00:08 We'll substitute appropriate values and solve for edge A

00:23 And this is the solution to the problem

Step-by-step written solution

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Understand the problem

A cube has a volume of 343 cm³.

How long are the cube's edges?

Step-by-step solution

To solve this problem, we'll use the relationship between the volume of a cube and its edge length, given by the formula:

$V = s^3$

where $V$ is the volume and $s$ is the edge length.

We are given that the volume of the cube is 343 cm³. We need to solve for the edge length $s$ :

$s^3 = 343$

To find $s$ , we take the cube root of both sides of the equation:

$s = \sqrt[3]{343}$

We need to determine the cube root of 343. Knowing that $7 \times 7 \times 7 = 343$ , we find:

$s = 7$ cm

Therefore, the length of each edge of the cube is $7$ cm.

Final Answer

$7$ cm

Key Points to Remember

Essential concepts to master this topic

Volume Formula: Cube volume equals side length cubed: $V = s^3$
Cube Root: Find $\sqrt[3]{343}$ by testing: $7 \times 7 \times 7 = 343$
Verification: Check answer by cubing: $7^3 = 343$ cm³ matches given volume ✓

Common Mistakes

Avoid these frequent errors

Taking square root instead of cube root
Don't find $\sqrt{343} \approx 18.5$ cm = wrong answer! Volume uses all three dimensions, not just area. Always take the cube root $\sqrt[3]{343} = 7$ for cube problems.

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

How do I find cube roots without a calculator?

Look for perfect cubes you know! Try small numbers: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$ , $5^3 = 125$ , $6^3 = 216$ , $7^3 = 343$ .

Why is the formula V = s³ and not V = 3s?

A cube has three dimensions all the same length. Volume is length × width × height, so $s \times s \times s = s^3$ . The number 3 would only give you the perimeter of one face!

What if the volume isn't a perfect cube?

You'll get a decimal answer! Use a calculator to find the cube root, or estimate between known perfect cubes. For example, $\sqrt[3]{300}$ is between 6 and 7 since $6^3 = 216$ and $7^3 = 343$ .

How do I check if 343 is really 7³?

Multiply step by step: $7 \times 7 = 49$ , then $49 \times 7 = 343$ . You can also think of it as $7^2 \times 7 = 49 \times 7 = 343$ .

Do all cubes have whole number edge lengths?

No! Only when the volume is a perfect cube (like 1, 8, 27, 64, 125, 216, 343...) will you get a whole number edge length. Most real cubes have decimal measurements.

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