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

00:11 Let's start by finding the height of the box.

00:15 We'll use the formula that calculates the volume of a box.

00:19 Multiply width, height, and length together.

00:23 Next, we'll plug in the known values and solve for height, H.

00:39 To do this, we need to isolate height, H.

00:48 And that's how we find the height of the box!

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

Look at the cuboid below:

What is the volume of the cuboid?

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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