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

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

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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