Calculate Cube Volume: Finding Volume from 4 cm² Base Area

Q: Why can't I just use the area as the volume?

Area and volume measure different things! Base area (4 cm²) tells you the flat surface, but volume needs all three dimensions. You must find the side length first, then cube it.

Q: How do I know the side length from the area?

Since a cube's base is a perfect square, take the square root of the area: $ s = \sqrt{\text{area}} $. For 4 cm², the side length is $ \sqrt{4} = 2 $ cm.

Q: Why is the volume formula s³ and not s²?

Volume measures 3D space, so you need length × width × height. For a cube, all sides are equal (s), so volume = s × s × s = s³. The ³ means three dimensions!

Cube Volume with Base Area

Shown below is a cube with a base of 4 cm².

Is it possible to calculate the volume of the cube? If so, then what is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Can we find the volume of the cube?

00:12 In a cube, all edges are the same. We'll call this edge 'A'.

00:17 Now, let's calculate the area of the cube's base.

00:21 Next, we'll focus on the cube's height, which is also 'A'.

00:25 We'll find the potential solutions by taking the cube root.

00:28 Remember, 'A' must be positive since it represents the edge's length.

00:33 Let's use the volume formula: edge length raised to the power of three, or A cubed.

00:39 Substitute the value of 'A' into the formula and calculate the volume.

00:44 And that's how we find the cube's volume!

Step-by-step written solution

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Understand the problem

Shown below is a cube with a base of 4 cm².

Is it possible to calculate the volume of the cube? If so, then what is it?

Step-by-step solution

To solve this problem, we'll determine if we can calculate the volume of the cube and, if possible, proceed with the calculation.

First, we need to find the side length of the cube. The given area of the base is $4 \, \text{cm}^2$ , indicating that each face of the cube is a square. Thus, we have:

$s^2 = 4$

To find $s$ , the side length $s$ , we take the square root of both sides:

$s = \sqrt{4} = 2 \, \text{cm}$

Now that we know the side length, we can calculate the volume of the cube using the formula:

$V = s^3 = 2^3 = 8 \, \text{cm}^3$

Therefore, it is indeed possible to calculate the volume of the cube. The volume is $8 \, \text{cm}^3$ .

The correct choice, reflecting this calculation, is $\boxed{8}$ .

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: From square base area, find side length first
Technique: If base = 4 cm², then s = √4 = 2 cm
Check: Volume s³ = 2³ = 8 cm³, so 2×2×2 = 8 ✓

Common Mistakes

Avoid these frequent errors

Using area directly as volume
Don't confuse base area with volume = 4 cm³ instead of 8 cm³! Area measures flat surface, volume measures 3D space. Always find side length first (√area), then cube it for volume (s³).

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 can't I just use the area as the volume?

Area and volume measure different things! Base area (4 cm²) tells you the flat surface, but volume needs all three dimensions. You must find the side length first, then cube it.

How do I know the side length from the area?

Since a cube's base is a perfect square, take the square root of the area: $s = \sqrt{\text{area}}$ . For 4 cm², the side length is $\sqrt{4} = 2$ cm.

What if the square root doesn't come out evenly?

That's fine! Use the exact square root in your calculation. For example, if area = 5 cm², then $s = \sqrt{5}$ cm and volume = $(\sqrt{5})^3 = 5\sqrt{5}$ cm³.

Why is the volume formula s³ and not s²?

Volume measures 3D space, so you need length × width × height. For a cube, all sides are equal (s), so volume = s × s × s = s³. The ³ means three dimensions!

How can I double-check my volume answer?

Verify that your side length squared equals the given base area: $2^2 = 4$ cm² ✓. Then check units: area is cm², volume should be cm³.

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