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

Question

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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Video Solution

Solution Steps

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 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=4×4×8 V = 4 \times 4 \times 8 .

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

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

Answer

256 256