Calculate Cube Volume: Finding Volume with 0.5 cm Edge Length

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

A cube has three dimensions - length, width, and height. To find volume, you multiply all three: 0.5 × 0.5 × 0.5. Since all sides are equal in a cube, this becomes $ 0.5^3 $!

Q: How do I convert 0.125 to a fraction?

Think: 0.125 = $ \frac{125}{1000} $. Then simplify by dividing both numbers by their greatest common factor (125): $ \frac{125 ÷ 125}{1000 ÷ 125} = \frac{1}{8} $

Q: What if I get confused with the decimal calculations?

Try working with fractions from the start! Since 0.5 = $ \frac{1}{2} $, you can calculate $ \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} $ directly.

Q: Why is the volume so much smaller than the side length?

When you cube a number less than 1, it gets smaller! For example: $ 0.5^3 = 0.125 $ which is smaller than 0.5. This makes sense - tiny cubes have very small volumes.

Q: How can I double-check my volume calculation?

Substitute back: if volume = $ \frac{1}{8} $ cm³, then $ \sqrt[3]{\frac{1}{8}} $ should equal 0.5 cm. Since $ \sqrt[3]{\frac{1}{8}} = \frac{1}{2} = 0.5 $ ✓

Volume Calculation with Fractional Dimensions

The edges of a cube are 0.5 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 Edge length according to the given data

00:07 We'll use the formula for calculating cube volume (edge cubed)

00:12 We'll substitute the edge length and solve for the volume

00:19 And this is the solution to the problem

Step-by-step written solution

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Understand the problem

The edges of a cube are 0.5 cm long.

Calculate the volume of the cube.

Step-by-step solution

To solve this problem, we will calculate the volume of a cube using the standard formula for its volume:

Volume formula of a cube: $V = s^3$ , where $s$ is the side length.

Given that each edge of the cube is 0.5 cm, we substitute this value into the formula:

$V = (0.5 \, \text{cm})^3$

Calculating the cube of 0.5:

$0.5^3 = 0.5 \times 0.5 \times 0.5$

$= 0.25 \times 0.5$

$= 0.125 \, \text{cm}^3$

However, it is important to recognize that the calculations when simplified produce a fraction:

$0.125$ can be written in fraction form as $\frac{1}{8}$ .

Therefore, the volume of the cube is $\frac{1}{8} \, \text{cm}^3$ , which matches the given answer choice.

Final Answer

$\frac{1}{8}$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals side length cubed: V = s³
Calculation: Convert 0.5³ = 0.5 × 0.5 × 0.5 = 0.125
Check: Convert decimal 0.125 to fraction form: $\frac{1}{8}$ cm³ ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or forgetting to cube all dimensions
Don't just multiply 0.5 × 3 = 1.5 thinking you add the dimensions! This gives area, not volume. Always use V = s³ which means multiply the side length by itself three times: 0.5 × 0.5 × 0.5.

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

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

A cube has three dimensions - length, width, and height. To find volume, you multiply all three: 0.5 × 0.5 × 0.5. Since all sides are equal in a cube, this becomes $0.5^3$ !

How do I convert 0.125 to a fraction?

Think: 0.125 = $\frac{125}{1000}$ . Then simplify by dividing both numbers by their greatest common factor (125): $\frac{125 ÷ 125}{1000 ÷ 125} = \frac{1}{8}$

What if I get confused with the decimal calculations?

Try working with fractions from the start! Since 0.5 = $\frac{1}{2}$ , you can calculate $\left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8}$ directly.

Why is the volume so much smaller than the side length?

When you cube a number less than 1, it gets smaller! For example: $0.5^3 = 0.125$ which is smaller than 0.5. This makes sense - tiny cubes have very small volumes.

How can I double-check my volume calculation?

Substitute back: if volume = $\frac{1}{8}$ cm³, then $\sqrt[3]{\frac{1}{8}}$ should equal 0.5 cm. Since $\sqrt[3]{\frac{1}{8}} = \frac{1}{2} = 0.5$ ✓

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