Math Problem Statement
Choose which option shows the plan and which option shows the front elevation of this 3D shape.
Solution
To determine which option shows the plan and which shows the front elevation of the 3D shape, we need to analyze the given 3D figure carefully. Let's break it down:
Plan View:
- The "plan" is the view of the object when looking directly from above (top view). You only see the 2D layout of the blocks without height.
- In the 3D figure, if viewed from above, we would see a rectangular shape with the blocks laid out in an "L" configuration. The block on top of others will not be visible from this view, only its position in the horizontal plane.
Front Elevation View:
- The front elevation is the view when looking directly from the front (as indicated in the image by the arrow labeled "front").
- When viewed from the front, you will observe the height of the blocks stacked in front, and the arrangement will resemble a step-like shape with varying heights.
Matching with the Options:
-
Plan View: The 2D view from the top should resemble an "L" shape without showing any height.
- Option E shows an "L" shape similar to what we expect from the top view. Therefore, E represents the plan view.
-
Front Elevation: The view from the front should reveal the height, with a block stacked higher and others at a lower level.
- Option D clearly shows the block stacked higher in the center with others at the base level, which corresponds to the front view of the 3D shape. So, D represents the front elevation.
Final Answer:
- Plan View: Option E.
- Front Elevation: Option D.
Would you like more details or have any other questions about this?
Here are 5 related questions to deepen your understanding:
- What is the difference between a plan view and a front elevation in 3D modeling?
- How can you determine a side elevation view for this 3D shape?
- How would the top view change if an additional block was added on top of the shape?
- What is the best way to visualize 3D shapes when given 2D projections?
- How do architectural plans use these types of views for building designs?
Tip: When analyzing 3D objects, always check how the object's height and layout change depending on the angle from which you view it.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
3D Geometry
Orthographic Projections
Formulas
-
Theorems
-
Suitable Grade Level
Grades 6-8