Calculate Cube Side Length: Finding the Edge When Volume = 1331

Cube Root Operations with Perfect Cubes

The volume of the cube is equal to 1331.

Ho long is the side of the cube?

aaa

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find the length of the cube's edge.
00:09 We'll use the cube volume formula: edge to the power of three.
00:13 Now, let's plug in the values and solve for edge, A.
00:24 And, that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The volume of the cube is equal to 1331.

Ho long is the side of the cube?

aaa

2

Step-by-step solution

To solve this problem, we need to find the side length of the cube given that its volume is 1331 cubic units.

We use the formula for the volume of a cube:
V=a3 V = a^3

Here, the volume V V is 1331, so substituting into the formula gives:
1331=a3 1331 = a^3

To find a a , take the cube root of both sides:
a=13313 a = \sqrt[3]{1331}

Calculating the cube root, we find:
a=11 a = 11

Thus, the side length of the cube is 11\mathbf{11}. This corresponds to choice 3 from the options provided.

3

Final Answer

11

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume of a cube equals side length cubed: V = a³
  • Technique: Find cube root: 13313=11 \sqrt[3]{1331} = 11 since 11³ = 1331
  • Check: Verify by cubing: 11 × 11 × 11 = 1331 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to find square root instead of cube root
    Don't find √1331 = 36.48! This gives the wrong type of root for a 3D volume problem. Always remember that cube volume uses cube root: ∛1331 = 11.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

How do I know when to use cube root vs square root?

+

Use cube root for 3D volume problems (cubes, rectangular prisms) and square root for 2D area problems (squares, circles). Since this is a cube's volume, we need cube root!

What if I don't recognize 1331 as a perfect cube?

+

Try testing small whole numbers: 103=1000 10^3 = 1000 , 113=1331 11^3 = 1331 , 123=1728 12^3 = 1728 . Learning perfect cubes 1-15 helps solve these faster!

Can I use a calculator to find cube roots?

+

Yes! Look for a ∛x button, or use the power function: 13311/3 1331^{1/3} . But recognizing perfect cubes mentally is faster for tests.

Why is the answer exactly 11 and not a decimal?

+

Because 1331 is a perfect cube! Perfect cubes always have whole number cube roots. This makes the math work out cleanly.

How can I remember the cube volume formula?

+

Think: "A cube has 3 dimensions, so I multiply the side length 3 times" - that's why it's a×a×a=a3 a \times a \times a = a^3 !

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Cuboids questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Cubes

Cube Surface Area 486: Calculate Side Length and Volume
Click to solve
Calculate Cube Side Length: Finding Edge Length for 27 cm³ Volume
Click to solve

Volume of a Orthohedron

Calculate Width X in a Cuboid: Given Volume 90, Height 5, Length 3
Click to solve
Solve for X in the Cuboid Volume Equation: 45 = 2.5 × 4 × X
Click to solve