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1.When creating a 3D shape with a given top view, what is the first essential step in the problem-solving process?()
A) Stack all cubes into a single column immediately.
B)Randomly place cubes without considering any view.
C) Construct the bottom layer according to the top view.
D) Only refer to the front view to build the shape.
2.For determining the number of different 3D shapes with a three-square top view and 4 cubes, how should you proceed?()
A) First set the bottom layer with three cubes (as the top view shows), then place the remaining cube on top of any of these three bottom cubes.
B) Change the top view to a different shape and then place the cubes.
C) Ignore the top view and stack all cubes in any way.
D) Only use two cubes for the bottom layer.
3. When identifying a 3D shape from top, front, and left views, what is a common wrong approach?()
A) Analyze the top view to define the bottom layer layout.
B) Disregard the top view and misarrange the base cubes.
C) Check if the front view’s layer heights match the shape.
D) Verify if the left view is consistent with the proposed shape.
4.In the process of determining a 3D shape from three views, which action correctly applies the problem-solving method?()
A) Start by using the top view to outline where the bottom layer cubes are placed.
B) Only consider the left view and ignore the other two views.
C) Guess the shape and then check if it fits the views.
D) Change the views to match a randomly chosen shape.
5. When solving the problem of finding the number of unpainted small cubes after painting the front and left sides of a rectangular prism, what is the crucial initial step?()
A) Count all small cubes directly without considering the painted regions.
B) Analyze which small cubes are painted on the front, left, and their overlapping part, then deduce the unpainted ones.
C) Randomly subtract a number from the total without any analysis.
D) Only focus on the bottom view and neglect the painted sides.
6.To determine the number of small cubes with exactly 2 faces painted when a large cube is divided into 64 small cubes, what reasoning is correct?()
A) Calculate the number of small cubes on each edge that are not at the corners (as corner cubes have 3 painted faces).
B) Count all surface cubes regardless of their position on edges or corners.
C) Presume each face has an equal number of 2-face painted cubes.
D) Only consider the central cubes of each face.
7. When identifying the front view of a 3D shape, what reasoning is accurate?()
A) Observe the shape from the front to determine the number of columns and layers.
B) Take the top view as the front view by mistake.
C) Draw cubes randomly after counting all of them in the shape.
D) Use the left view as the front view.
8. When figuring out the left view of a 3D shape, what common error should be prevented?()
A) Analyze the shape from the left direction to check the number of columns and layers.
B) Mix up the left view with the front view by observing from the wrong angle.
C) Count the number of cubes in each row from the left.
D) Verify if the layer count from the left aligns with the shape.
9.If a shape appears as a single square from the front, what is its key feature?()
A) It must be a single cube.
B) It can be multiple cubes arranged such that only one square is visible from the front (e.g., cubes stacked behind each other in the same column).
C) It needs to have three or more cubes in a row.
D) It must have cubes in multiple columns with only one column visible.
10.When finding a 3D shape that matches a given view from both the left and front sides, what is the essential action?()
A) Check the number of columns, layers, and their arrangement from both the left and front directions to match the given view.
B) Only look at the top view and ignore the left and front views.
C) Pick any shape and hope it matches the view.
D) Assume all shapes with the same number of cubes will fit the view.
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