Calculate Cuboid Volume: 8cm Square Base × 5cm Height

Q: Why do I square the base side length?

Because the base is a square! When you have a square with side length 8 cm, both length and width are 8 cm. So base area = $ 8 \times 8 = 8^2 = 64 \, \text{cm}^2 $.

Q: What's the difference between a cuboid and a cube?

A cube has all sides equal, while a cuboid can have different dimensions. This problem has a cuboid because the height (5 cm) is different from the base sides (8 cm).

Q: Can I just multiply 8 × 8 × 5 directly?

Absolutely! That's actually the most direct way. Volume = length × width × height = $ 8 \times 8 \times 5 = 320 \, \text{cm}^3 $. The two-step method just helps you understand the concept better.

Q: Why are the units cm³ and not cm²?

Volume measures three-dimensional space, so you need cubic units (cm³). Area uses square units (cm²) for flat surfaces, but volume fills up space in length, width, AND height.

Q: What if I forget to square the base?

You'd get $ 8 \times 5 = 40 \, \text{cm}^3 $ instead of 320 cm³ - way too small! Always remember that square base area means side × side, not just the side length.

Cuboid Volume with Square Base

Given an cuboid such that its base is a square.

The length of the side of the base is equal to 8 cm

The length of the height is equal to 5 cm

Find the volume of the cuboid

❤️ 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 the box volume

00:03 The base of the box is a square according to the given data, therefore the sides are equal

00:18 The side values according to the given data

00:24 We'll use the formula for calculating box volume

00:28 Height multiplied by length multiplied by width

00:32 We'll substitute appropriate values and solve to find the volume

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 an cuboid such that its base is a square.

The length of the side of the base is equal to 8 cm

The length of the height is equal to 5 cm

Find the volume of the cuboid

Step-by-step solution

To solve the problem of finding the volume of the given cuboid, we'll follow the outlined steps:

Step 1: Calculate the area of the base.
Step 2: Multiply the base area by the height to find the volume.

Now, let's work through each step:

Step 1: Calculate the area of the base.
The side length of the square base is given as 8 cm. The formula for the area of a square is $a^2$ , where $a$ is the side length. Substituting the value, we get:
$\text{Base Area} = 8^2 = 64 \, \text{cm}^2$

Step 2: Multiply the base area by the height.
The height of the cuboid is given as 5 cm. Using the formula for the volume of a cuboid $\text{Volume} = \text{Base Area} \times \text{Height}$ , we substitute the known values:
$\text{Volume} = 64 \, \text{cm}^2 \times 5 \, \text{cm} = 320 \, \text{cm}^3$

Therefore, the volume of the cuboid is $320 \, \text{cm}^3$ .

Final Answer

$320$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume = Base Area × Height for all cuboids
Technique: Square base area = $8^2 = 64 \, \text{cm}^2$ , then multiply by height
Check: Units should be cubic: $\text{cm}^2 \times \text{cm} = \text{cm}^3$ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add 8 + 8 + 5 = 21! This gives a length, not volume. Volume needs three dimensions multiplied together. Always use Volume = length × width × height = $8 \times 8 \times 5 = 320 \, \text{cm}^3$ .

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 I square the base side length?

Because the base is a square! When you have a square with side length 8 cm, both length and width are 8 cm. So base area = $8 \times 8 = 8^2 = 64 \, \text{cm}^2$ .

What's the difference between a cuboid and a cube?

A cube has all sides equal, while a cuboid can have different dimensions. This problem has a cuboid because the height (5 cm) is different from the base sides (8 cm).

Can I just multiply 8 × 8 × 5 directly?

Absolutely! That's actually the most direct way. Volume = length × width × height = $8 \times 8 \times 5 = 320 \, \text{cm}^3$ . The two-step method just helps you understand the concept better.

Why are the units cm³ and not cm²?

Volume measures three-dimensional space, so you need cubic units (cm³). Area uses square units (cm²) for flat surfaces, but volume fills up space in length, width, AND height.

What if I forget to square the base?

You'd get $8 \times 5 = 40 \, \text{cm}^3$ instead of 320 cm³ - way too small! Always remember that square base area means side × side, not just the side length.

🌟 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