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Isometric view of a stepped block with labeled dimensions and front elevation.

Technical drawing of a 3D mechanical component with dimensions and front elevation view.

Technical drawing of a 3D mechanical component with dimensions and front elevation view.

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Show Answer Key & Explanations Step-by-step solution for: First angle orthographic exercise 9

Problem Description:


The image shows a 3D object with dimensions provided. The task is to calculate the volume of the object. The object appears to be composed of multiple rectangular prisms stacked on top of each other, with some portions removed.

Step-by-Step Solution:



#### 1. Analyze the Structure:
The object can be broken down into simpler geometric shapes:
- A large base rectangular prism.
- A smaller rectangular prism on top of the base.
- A triangular prism-like structure extending from the top of the smaller rectangular prism.

#### 2. Calculate the Volume of Each Part:

##### Part 1: Base Rectangular Prism
- Dimensions: \(60 \times 60 \times 40\) (length × width × height).
- Volume of a rectangular prism: \( V = \text{length} \times \text{width} \times \text{height} \).
- Volume of the base:
\[
V_{\text{base}} = 60 \times 60 \times 40 = 144,000 \, \text{cubic units}.
\]

##### Part 2: Smaller Rectangular Prism on Top
- Dimensions: \(60 \times 60 \times 20\) (length × width × height).
- Volume of the smaller rectangular prism:
\[
V_{\text{small}} = 60 \times 60 \times 20 = 72,000 \, \text{cubic units}.
\]

##### Part 3: Triangular Prism-Like Extension
- The extension forms a triangular prism that extends outward from the top of the smaller rectangular prism.
- Dimensions:
- Height of the triangular prism: \(20\) (same as the height of the smaller rectangular prism).
- Base of the triangular prism: A right triangle with legs of \(20\) and \(20\).
- Area of the triangular base:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 20 = 200 \, \text{square units}.
\]
- Volume of the triangular prism:
\[
V_{\text{triangular prism}} = \text{Area of base} \times \text{height} = 200 \times 20 = 4,000 \, \text{cubic units}.
\]

#### 3. Total Volume Calculation:
The total volume of the object is the sum of the volumes of all parts:
\[
V_{\text{total}} = V_{\text{base}} + V_{\text{small}} + V_{\text{triangular prism}}.
\]
Substitute the values:
\[
V_{\text{total}} = 144,000 + 72,000 + 4,000 = 220,000 \, \text{cubic units}.
\]

Final Answer:


\[
\boxed{220000}
\]
Parent Tip: Review the logic above to help your child master the concept of orthographic projection worksheet.
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