Calculate Cuboid Height: Given Length 5cm, Width 3cm, Volume 30cm³

Q: Why do we multiply the dimensions instead of adding them?

Volume measures space inside a 3D shape! Think of it as counting unit cubes that fit inside. When you have 5 cubes along length, 3 along width, you get 5 × 3 = 15 cubes per layer. Then multiply by height layers.

Q: How is this different from finding area?

Area is 2-dimensional (Length × Width), but volume is 3-dimensional (Length × Width × Height). Volume tells you how much space is inside the cuboid.

Q: Can I solve this problem in a different order?

Yes! You can find $ L \times W = 5 \times 3 = 15 $ first, then calculate $ H = \frac{30}{15} = 2 $. The math is the same!

Q: What units should my answer have?

Since length and width are in cm, and volume is in cm³, your height must also be in cm. Always match the units given in the problem.

Volume Formula with Missing Dimension

Given the length of the cuboid is 5 cm

Width is equal to 3 cm

Volume of the cuboid is equal to 30 cm3

Calculate the height of the cuboid

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the height of the box

00:03 We'll use the formula for calculating box volume

00:07 width times height times length

00:11 We'll substitute appropriate values and solve for height H

00:28 We'll isolate height H

00:37 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

Given the length of the cuboid is 5 cm

Width is equal to 3 cm

Volume of the cuboid is equal to 30 cm3

Calculate the height of the cuboid

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us:
- Length ( $L$ ) = $5 \, \text{cm}$
- Width ( $W$ ) = $3 \, \text{cm}$
- Volume ( $V$ ) = $30 \, \text{cm}^3$

Step 2: We'll use the formula:

$V = L \times W \times H$

Step 3: Plug in the known values:

$30 = 5 \times 3 \times H$

Simplify the equation:

$30 = 15 \times H$

To solve for $H$ , divide both sides by 15:

$H = \frac{30}{15} = 2 \, \text{cm}$

Therefore, the height of the cuboid is $2 \, \text{cm}$ .

Final Answer

2 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cuboid equals length × width × height
Technique: Rearrange V = L × W × H to H = V ÷ (L × W)
Check: Substitute back: 5 × 3 × 2 = 30 cm³ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 5 + 3 + H = 30 giving H = 22 cm! Volume requires multiplication of all three dimensions, not addition. Always use V = L × W × H for cuboids.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

Why do we multiply the dimensions instead of adding them?

Volume measures space inside a 3D shape! Think of it as counting unit cubes that fit inside. When you have 5 cubes along length, 3 along width, you get 5 × 3 = 15 cubes per layer. Then multiply by height layers.

What if I get a decimal answer for height?

Decimal heights are perfectly normal! Just make sure your calculation is correct: H = Volume ÷ (Length × Width). Always double-check by multiplying back.

How is this different from finding area?

Area is 2-dimensional (Length × Width), but volume is 3-dimensional (Length × Width × Height). Volume tells you how much space is inside the cuboid.

Can I solve this problem in a different order?

Yes! You can find $L \times W = 5 \times 3 = 15$ first, then calculate $H = \frac{30}{15} = 2$ . The math is the same!

What units should my answer have?

Since length and width are in cm, and volume is in cm³, your height must also be in cm. Always match the units given in the problem.

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Calculate Cuboid Height: Given Length 5cm, Width 3cm, Volume 30cm³

Volume Formula with Missing Dimension

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we multiply the dimensions instead of adding them?

What if I get a decimal answer for height?

How is this different from finding area?

Can I solve this problem in a different order?

What units should my answer have?

🌟 Unlock Your Math Potential

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