Calculate Sand Height in a 64 cm³ Cube: Volume to Height Conversion

Q: Why do I need to find the cube's side length first?

You need the side length to calculate the base area! Since the cube has volume 64 cm³, each side is $ \sqrt[3]{64} = 4 $ cm, giving you a base area of 16 cm².

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

They're exactly the same! 1 cc = 1 cm³. Both measure volume, so 32 cc of sand equals 32 cm³ of sand.

Q: How do I know the sand spreads evenly?

The problem assumes the sand spreads uniformly across the entire bottom of the cube. This means it forms a flat, even layer with consistent height everywhere.

Q: What if the sand volume was bigger than the cube?

If you had more than 64 cm³ of sand, it wouldn't fit! The maximum height is 4 cm (the cube's full height), so you can only fit up to 64 cm³ total.

Q: Can I use this method for other shapes?

Yes! For any container, height = volume ÷ base area. Just make sure you can calculate the base area correctly for that shape.

Q: How do I check if my answer makes sense?

Ask yourself: Is the height reasonable? Since the cube is 4 cm tall and you're filling it halfway with sand, 2 cm height makes perfect sense!

Volume Calculations with Cube Dimensions

Below is a cube with a volume equal to 64 cm3.

If we pour 32 cc of sand into the cube, how high will the sand reach?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What height will the sand reach?

00:03 We'll use the formula for volume calculation (edge cubed)

00:07 We'll take the cube root

00:13 This is the edge length of the cube

00:16 The height is the edge of the cube

00:20 We'll calculate the volume ratio between the sand and the cube

00:25 This is the volume ratio

00:30 We'll multiply this ratio by height to find the sand height

00:33 We'll substitute the height value we found and solve to find the sand height

00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a cube with a volume equal to 64 cm3.

If we pour 32 cc of sand into the cube, how high will the sand reach?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Calculate the side length of the cube.
- The volume of the cube is $64 \, \text{cm}^3$ . Using the formula for the volume of a cube, $s^3 = 64$ .
- Find $s$ : $s = \sqrt[3]{64} = 4 \, \text{cm}$ .
Step 2: Determine the base area of the cube.
- The base of the cube is a square with side length $4 \, \text{cm}$ .
- The area, $A_{\text{base}}$ , is $4 \, \text{cm} \times 4 \, \text{cm} = 16 \, \text{cm}^2$ .
Step 3: Calculate the height the sand will reach.
- We have $32 \, \text{cm}^3$ of sand. Use the volume formula for height: $32 = 16 \times h$ .
- Solve for $h$ : $h = \frac{32}{16} = 2 \, \text{cm}$ .

Therefore, the sand will reach a height of $2 \, \text{cm}$ in the cube.

Final Answer

$2$ cm

Key Points to Remember

Essential concepts to master this topic

Cube Volume Rule: Volume equals side length cubed, so $s^3 = 64$ means $s = 4$ cm
Height Formula: For rectangular containers, height = volume ÷ base area = $\frac{32}{16} = 2$ cm
Check Method: Verify by calculating: base area × height = $16 \times 2 = 32$ cm³ ✓

Common Mistakes

Avoid these frequent errors

Using total cube volume instead of sand volume for height calculation
Don't divide the sand volume (32 cm³) by the cube's total volume (64 cm³) = meaningless ratio! This confuses volume with height and gives wrong answers. Always divide the sand volume by the base area to find height.

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

Why do I need to find the cube's side length first?

You need the side length to calculate the base area! Since the cube has volume 64 cm³, each side is $\sqrt[3]{64} = 4$ cm, giving you a base area of 16 cm².

What's the difference between cc and cm³?

They're exactly the same! 1 cc = 1 cm³. Both measure volume, so 32 cc of sand equals 32 cm³ of sand.

How do I know the sand spreads evenly?

The problem assumes the sand spreads uniformly across the entire bottom of the cube. This means it forms a flat, even layer with consistent height everywhere.

What if the sand volume was bigger than the cube?

If you had more than 64 cm³ of sand, it wouldn't fit! The maximum height is 4 cm (the cube's full height), so you can only fit up to 64 cm³ total.

Can I use this method for other shapes?

Yes! For any container, height = volume ÷ base area. Just make sure you can calculate the base area correctly for that shape.

How do I check if my answer makes sense?

Ask yourself: Is the height reasonable? Since the cube is 4 cm tall and you're filling it halfway with sand, 2 cm height makes perfect sense!

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