Find Side Length HF in a Cuboid with Volume 60 cm³

Q: What if I can't see all the measurements in the diagram?

Look carefully at the diagram for labeled edges. In this problem, you can see '4' and '5' marked on different edges. The third dimension is what you need to find using the volume formula.

Q: How do I solve 20x = 60 quickly?

Divide both sides by 20: x = 60 ÷ 20 = 3. You can also think: "What times 20 equals 60?" Since 20 × 3 = 60, the answer is 3.

Q: What units should my answer have?

Since the volume is in cm³ and the other sides are in cm, your answer will also be in cm. Length measurements use linear units (cm), while volume uses cubic units (cm³).

Volume Formula with Unknown Side Length

Look at the following cuboid.

The volume of the cuboid is 60 cm³.

What is the length of the side HF?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find HF

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

00:08 height times length times width

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

00:36 Isolate HF

00:44 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

Look at the following cuboid.

The volume of the cuboid is 60 cm³.

What is the length of the side HF?

Step-by-step solution

To find the length of side HF, follow these steps:

Step 1: Identify known values - Volume $V = 60 \, \text{cm}^3$ , given side lengths are 4 cm and 5 cm.
Step 2: Apply the volume formula for a cuboid: $V = l \times w \times h$ , with two sides known as 4 cm and 5 cm.
Step 3: Set up the equation using $x$ as the unknown side: $4 \times 5 \times x = 60$ .
Step 4: Solve for $x$ :
$20 \times x = 60$
Divide both sides by 20: $x = \frac{60}{20} = 3$ .

Thus, the length of side HF is $3 \, \text{cm}$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume = length × width × height for cuboids
Technique: Substitute known values: 4 × 5 × x = 60
Check: Verify by calculating: 4 × 5 × 3 = 60 cm³ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add the three dimensions like 4 + 5 + x = 60! This gives x = 51 cm, which is impossibly large. Volume always requires multiplication because you're finding the space inside. Always multiply all three dimensions: length × width × height.

Practice Quiz

Test your knowledge with interactive questions

Calculate the volume of the rectangular prism below using the data provided.

FAQ

Everything you need to know about this question

How do I know which sides are length, width, and height?

It doesn't matter which dimension you call length, width, or height! In a cuboid, volume = side₁ × side₂ × side₃ regardless of labeling. Just multiply all three dimensions together.

What if I can't see all the measurements in the diagram?

Look carefully at the diagram for labeled edges. In this problem, you can see '4' and '5' marked on different edges. The third dimension is what you need to find using the volume formula.

Can the unknown side be a decimal?

Yes! Side lengths can be decimals. However, in this problem, 60 ÷ (4 × 5) = 60 ÷ 20 = 3, which gives us a whole number answer.

How do I solve 20x = 60 quickly?

Divide both sides by 20: x = 60 ÷ 20 = 3. You can also think: "What times 20 equals 60?" Since 20 × 3 = 60, the answer is 3.

What units should my answer have?

Since the volume is in cm³ and the other sides are in cm, your answer will also be in cm. Length measurements use linear units (cm), while volume uses cubic units (cm³).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Cuboids questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime