Problem Analysis:
The image depicts a 3D object with a front elevation shown. The task is to determine the volume of the object. Let us break this down step by step.
#### Key Observations:
1.
Overall Dimensions:
- The outer dimensions of the object are \(40 \times 40 \times 40\) (length, width, height).
- The object has a hollow section in the middle, which is structured like a staircase.
2.
Staircase Structure:
- The hollow section consists of three steps.
- Each step has a depth of \(20\) units and a height of \(20\) units.
- The width of each step is also \(20\) units.
3.
Volume Calculation Approach:
- Calculate the total volume of the outer cube.
- Subtract the volume of the hollow staircase section.
---
Step-by-Step Solution:
#### 1. Volume of the Outer Cube
The outer cube has dimensions \(40 \times 40 \times 40\). The volume \(V_{\text{outer}}\) is calculated as:
\[
V_{\text{outer}} = 40 \times 40 \times 40 = 64000 \, \text{cubic units}
\]
#### 2. Volume of the Hollow Staircase Section
The hollow section consists of three steps. Each step is a rectangular prism with dimensions:
- Length = \(20\) units (depth of the step)
- Width = \(20\) units (width of the step)
- Height = \(20\) units (height of the step)
The volume of one step is:
\[
V_{\text{step}} = 20 \times 20 \times 20 = 8000 \, \text{cubic units}
\]
Since there are three steps, the total volume of the hollow section is:
\[
V_{\text{hollow}} = 3 \times V_{\text{step}} = 3 \times 8000 = 24000 \, \text{cubic units}
\]
#### 3. Volume of the Object
The volume of the object is the volume of the outer cube minus the volume of the hollow section:
\[
V_{\text{object}} = V_{\text{outer}} - V_{\text{hollow}} = 64000 - 24000 = 40000 \, \text{cubic units}
\]
---
Final Answer:
\[
\boxed{40000}
\]
Parent Tip: Review the logic above to help your child master the concept of orthographic projection worksheet.
