Calculate Volume of 5×(5,6,8) Meter Cuboid Assembly: Composite Structure Problem

The dimensions of the cuboid are 5,6,8 meters

From five orthohedra of the same size we build the body in the drawing.

Calculates the volume of the created body

Video Solution

Solution Steps

00:00 Calculate the volume of the shared body

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

00:06 Height times length times width

00:10 We'll substitute appropriate values and solve for the volume

00:15 This is the volume of one box, now we'll multiply this volume by the number of boxes

00:28 And this is the solution to the problem

Step-by-Step Solution

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

Let's proceed:

Step 1: For a single orthohedron with dimensions of 5 meters, 6 meters, and 8 meters, the volume is calculated using:

$\text{Volume of one orthohedron} = 5 \times 6 \times 8$

This equates to $5 \times 6 = 30$ , and then $30 \times 8 = 240$ . Therefore, the volume of one orthohedron is $240 \, \text{cubic meters}$ .

Step 2: Since there are five such orthohedra forming the complete body, multiply the volume of one by 5:

$\text{Total volume} = 5 \times 240 = 1200 \, \text{cubic meters}$

Thus, the total volume of the created body is $1200 \, \text{cubic meters}$ .

The correct choice that corresponds to this volume is:

Therefore, the solution to the problem is $1200$ .