Volume Calculation: 4m × 8m Square-Based Cuboid Construction Problem

Q: What does 'square-based cuboid' mean exactly?

A square-based cuboid has a square for its base. Since one dimension is 4 meters, the base is 4 × 4 square meters, not 4 × 8!

Q: Why do we multiply by 2 at the end?

The problem states we're using two identical cuboids to build the final shape. Since each has volume 128 cubic meters, the total is $ 2 \times 128 = 256 $ cubic meters.

Q: Can I solve this by adding the dimensions differently?

No! Volume formulas are specific. For a cuboid, you must use length × width × height. You can't just add or rearrange dimensions randomly.

Q: What if the drawing shows something different than I calculated?

Trust the mathematical calculation over visual interpretation. The drawing helps visualize the problem, but the dimensions given in the text (4 and 8 meters) are what you use for calculations.

Cuboid Volume with Combined Shapes

The dimensions of a square-based cuboid are 4 and 8 meters.

From two orthohedra of the same size we build the bodand in the drawing.

Find the volume of the created bodand

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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 shared body

00:03 Square base according to the data, therefore equal sides

00:07 We'll use the formula for calculating box volume

00:10 height times length times width

00:14 We'll substitute appropriate values and solve for the volume

00:20 This is the volume of one box, now we'll multiply this volume by the number of boxes

00:29 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

The dimensions of a square-based cuboid are 4 and 8 meters.

From two orthohedra of the same size we build the bodand in the drawing.

Find the volume of the created bodand

Step-by-step solution

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

Step 1: Determine individual cuboid dimensions and calculate its volume
Step 2: Calculate the cumulative volume resulting from the merger of two identical cuboids

Let's work through these steps:
Step 1: The given dimensions for a square-based cuboid suggest each has a base of 4 meters and a height of 8 meters. Therefore, the volume of one cuboid is determined using the formula: $V = 4 \times 4 \times 8$ .

Calculating this gives: $V = 128 \text{ cubic meters}$ .
Step 2: Since two such cuboids are combined to form the bodand, the total volume is: $2 \times 128 = 256 \text{ cubic meters}$ .

Therefore, the volume of the created bodand is $256 \text{ cubic meters}$ .

Final Answer

$256$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cuboid equals length × width × height
Technique: Calculate individual volume first: $4 \times 4 \times 8 = 128$ cubic meters
Check: Total volume equals two identical cuboids: $2 \times 128 = 256$ ✓

Common Mistakes

Avoid these frequent errors

Confusing dimensions and calculating wrong base area
Don't assume the base is 4 × 8 = 32 square meters! This gives volume of 4 × 8 × 8 = 256 for one cuboid, doubling to 512. Always identify that 'square-based' means the base is 4 × 4 = 16 square meters.

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

What does 'square-based cuboid' mean exactly?

A square-based cuboid has a square for its base. Since one dimension is 4 meters, the base is 4 × 4 square meters, not 4 × 8!

How do I know which dimension is the height?

With dimensions 4 and 8 meters for a square-based cuboid, the 4 meters is the side of the square base, and the 8 meters is the height. The base area is 4 × 4 = 16 square meters.

Why do we multiply by 2 at the end?

The problem states we're using two identical cuboids to build the final shape. Since each has volume 128 cubic meters, the total is $2 \times 128 = 256$ cubic meters.

Can I solve this by adding the dimensions differently?

No! Volume formulas are specific. For a cuboid, you must use length × width × height. You can't just add or rearrange dimensions randomly.

What if the drawing shows something different than I calculated?

Trust the mathematical calculation over visual interpretation. The drawing helps visualize the problem, but the dimensions given in the text (4 and 8 meters) are what you use for calculations.

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