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

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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

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

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.

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