Calculate Cuboid Volume: 5cm × 4cm with 94cm² Surface Area

Q: Why do we need to find the height first before calculating volume?

We need all three dimensions to calculate volume! Since we only know length (5 cm) and width (4 cm), we must use the surface area to find the missing height dimension first.

Q: What does the 2 in the surface area formula represent?

The factor of 2 accounts for opposite faces being identical! A cuboid has 6 faces that come in 3 pairs: top/bottom (lw), front/back (lh), and left/right (wh).

Q: How do I combine like terms when solving for h?

Look for terms with the same variable: 5h + 4h = 9h. Think of it as having 5 apples plus 4 apples = 9 apples, but with h instead of apples!

Q: Can I check my answer without doing the full calculation again?

Yes! Use the surface area formula: $ 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2(47) = 94 $ ✓

Q: What if I get a decimal or fraction for the height?

That's completely normal! Real-world problems often have non-integer dimensions. Just make sure to use the exact value (not rounded) when calculating the final volume.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's figure out the volume of the box.

00:14 First, we'll find the surface area of a box. Here's how!

00:22 Add up the areas of three rectangles. Then double it.

00:27 Calculate each rectangle's area. Side times side. Easy!

00:32 Now, plug in the numbers given in the problem. Let's solve for H, the height.

00:58 Next, we'll isolate H on one side to find the height.

01:14 Great! We've found the height H of our box!

01:21 Now, let's work on the box's volume using a formula.

01:25 Multiply width by height by length. That's the formula.

01:29 Substitute the height H we found to get the volume.

01:33 And there you have it. We've solved the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Given the surface area of the cuboid equal to 94 cm.3

The length of the cuboid is 5 cm. and its width 4 cm.

Calculate the volume of the cube

2

Step-by-step solution

To solve this problem, we are going to determine the volume of a cuboid given its length, width, and overall surface area. Here's how we will do it:

Firstly, calculate the height $h$ of the cuboid using the surface area formula.
Then, use the calculated height to determine the volume of the cuboid.

Now, let's work through each step:

Step 1: Calculate the height $h$ .

We know the surface area of a cuboid is given by the formula:

2(lw + lh + wh) = \text{Surface Area}

Substituting the known values:

2(5 \cdot 4 + 5 \cdot h + 4 \cdot h) = 94

Simplify:

2(20 + 5h + 4h) = 94

2(20 + 9h) = 94

Divide both sides by 2:

20 + 9h = 47

Simplify further to solve for $h$ :

9h = 27

h = 3 \, \text{cm}

Step 2: Calculate the volume using the height $h$ .

Now that we know $h = 3 \, \text{cm}$ , use the volume formula for the cuboid:

\text{Volume} = l \times w \times h

\text{Volume} = 5 \times 4 \times 3 = 60 \, \text{cm}^3

Therefore, the volume of the cuboid is $\mathbf{60 \, \text{cm}^3}$ .

3

Final Answer

60 cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Cuboid surface area = 2(lw + lh + wh)
Technique: Substitute known values: 2(5×4 + 5h + 4h) = 94
Check: Volume = 5×4×3 = 60 cm³ with height h = 3 cm ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply surface area formula by 2
Don't use lw + lh + wh = 94 directly = wrong height calculation! This gives h = 7 instead of h = 3, leading to volume = 140 cm³ instead of 60 cm³. Always remember the surface area formula has a factor of 2.

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 need to find the height first before calculating volume?

+

We need all three dimensions to calculate volume! Since we only know length (5 cm) and width (4 cm), we must use the surface area to find the missing height dimension first.

What does the 2 in the surface area formula represent?

+

The factor of 2 accounts for opposite faces being identical! A cuboid has 6 faces that come in 3 pairs: top/bottom (lw), front/back (lh), and left/right (wh).

How do I combine like terms when solving for h?

+

Look for terms with the same variable: 5h + 4h = 9h. Think of it as having 5 apples plus 4 apples = 9 apples, but with h instead of apples!

Can I check my answer without doing the full calculation again?

+

Yes! Use the surface area formula: $2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2(47) = 94$ ✓

What if I get a decimal or fraction for the height?

+

That's completely normal! Real-world problems often have non-integer dimensions. Just make sure to use the exact value (not rounded) when calculating the final volume.

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Calculate Cuboid Volume: 5cm × 4cm with 94cm² Surface Area

Surface Area Formula with Unknown Dimension

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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 need to find the height first before calculating volume?

What does the 2 in the surface area formula represent?

How do I combine like terms when solving for h?

Can I check my answer without doing the full calculation again?

What if I get a decimal or fraction for the height?

🌟 Unlock Your Math Potential

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