Calculate the Volume: Cuboid with Dimensions 4×2×5 Containing Equal Parts

Q: Why do I multiply by 5 at the end?

The problem states there are 5 smaller cuboids of equal size inside the large cuboid. Since each small cuboid has volume $ 40 \, \text{cm}^3 $, the total is $ 5 \times 40 = 200 \, \text{cm}^3 $.

Q: What if the small cuboids weren't equal in size?

Then you'd need to calculate the volume of each different cuboid separately and add them all together. But this problem specifically says they're equal size, so we can use multiplication as a shortcut!

Q: Why is the answer in cubic centimeters?

Volume is always measured in cubic units. Since the dimensions are in centimeters, the volume is in cubic centimeters ($ \text{cm}^3 $). This shows we're measuring 3-dimensional space!

Q: Can I solve this by finding the large cuboid's dimensions directly?

Yes! The large cuboid would be $ 4 \times 2 \times 25 $ (since 5 equal pieces of height 5 each = total height 25). Either method gives $ 200 \, \text{cm}^3 $!

Volume Calculation with Multiple Equal Cuboids

Shown below is a cuboid containing 5 smaller cuboids of equal size.

AB = 4

BE = 2

EK = 5

Calculate the volume of the large cuboid.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the volume of the large box

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

00:07 width times height times length

00:12 We'll substitute appropriate values and solve for the volume

00:23 This is the volume of the small box

00:26 The volume of the large box equals 5 times the volume of the small box

00:37 We'll substitute the value of the small box volume and solve for the volume

00:40 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

Shown below is a cuboid containing 5 smaller cuboids of equal size.

AB = 4

BE = 2

EK = 5

Calculate the volume of the large cuboid.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the volume of one smaller cuboid.
Step 2: Multiply the volume of one smaller cuboid by the number of cuboids (5) to find the total volume of the large cuboid.

Now, let's work through each step:
Step 1: The dimensions for each smaller cuboid are given as:

Length: $4 \, \text{cm}$
Width: $2 \, \text{cm}$
Height: $5 \, \text{cm}$

Using the volume formula for a cuboid, we find the volume of one smaller cuboid:

V_{\text{small}} = 4 \times 2 \times 5 = 40 \, \text{cm}^3

Step 2: Since there are 5 such smaller cuboids, the total volume for the large cuboid is:

V_{\text{large}} = 5 \times 40 = 200 \, \text{cm}^3

Therefore, the volume of the large cuboid is $200 \, \text{cm}^3$ .

Final Answer

200 cm³

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For any cuboid, multiply length × width × height
Technique: Calculate one cuboid: $4 \times 2 \times 5 = 40 \, \text{cm}^3$
Check: Total volume should equal single volume × number of parts: $40 \times 5 = 200 \, \text{cm}^3$ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 4 + 2 + 5 = 11 for volume! This gives a linear measurement, not cubic volume. Always multiply all three dimensions: length × width × height to get cubic units.

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 multiply by 5 at the end?

The problem states there are 5 smaller cuboids of equal size inside the large cuboid. Since each small cuboid has volume $40 \, \text{cm}^3$ , the total is $5 \times 40 = 200 \, \text{cm}^3$ .

What if the small cuboids weren't equal in size?

Then you'd need to calculate the volume of each different cuboid separately and add them all together. But this problem specifically says they're equal size, so we can use multiplication as a shortcut!

How do I know which dimensions go with length, width, and height?

It doesn't matter which dimension you call length, width, or height! Volume is always all three dimensions multiplied together, regardless of the order: $4 \times 2 \times 5 = 2 \times 5 \times 4 = 40$ .

Why is the answer in cubic centimeters?

Volume is always measured in cubic units. Since the dimensions are in centimeters, the volume is in cubic centimeters ( $\text{cm}^3$ ). This shows we're measuring 3-dimensional space!

Can I solve this by finding the large cuboid's dimensions directly?

Yes! The large cuboid would be $4 \times 2 \times 25$ (since 5 equal pieces of height 5 each = total height 25). Either method gives $200 \, \text{cm}^3$ !

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