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Questions and Answers

Given the orthogonal projections (plan and side elevation) of a solid, which of the following axonometric projections accurately represents it?

diagram of solid (correct)
diagram of solid (correct)
diagram of solid (correct)
diagram of solid (correct)
diagram of solid (correct)

Which of the solid figures below, when inverted and joined to the figure above, would reconstruct a complete cube?

object (correct)
object (correct)
object (correct)
object (correct)
object (correct)

Match the isometric views with their corresponding orthographic projections, identifying the correct association for each numbered isometric view to its lettered orthographic projection.

1 - d; 2 - c; 3 - a; 4 - e; 5 - b
1 - c; 2 - d; 3 - a; 4 - e; 5 - b
1 - c; 2 - d; 3 - a; 4 - b; 5 - e (correct)
1 - a; 2 - b; 3 - c; 4 - d; 5 - e
1 - c; 2 - d; 3 - e; 4 - a; 5 - b

Which of the following statements regarding standard paper sizes is NOT correct?

A sheet of A0 size is equivalent to four A3 sheets. (D) Signup and view all the answers

Match the cut cones to their corresponding flattened development.

1-e; 2-d; 3 - a; 4 - b; 5 - c (A) Signup and view all the answers

Identify the correct axonometric projection of the solid shown in the figure.

image (A), image (B), image (C), image (D), image (E) Signup and view all the answers

Referring to a plane that intersects a set of solids (three steps, two cubic blocks on top of the final step) identify the correct cross-section in orthographic projection.

two rectangles with sides attached (D) Signup and view all the answers

Referring to the section plane cutting through the composition of solids represented in plan and elevation, identify the correct sectioned plan view.

diagram of shape (A), diagram of shape (B), diagram of shape (C), diagram of shape (D), diagram of shape (E) Signup and view all the answers

Given two views of a cube with figures on its faces, identify the correct unfolded net of the cube.

Net of a cube option A (E) Signup and view all the answers

Consider a pattern consisting of repeating geometric shapes. If each shape incrementally rotates 30 degrees clockwise compared to the previous one, how many shapes are needed for the pattern to return to its original orientation?

12 (A) Signup and view all the answers

Considering a standard Cartesian coordinate system, which of the following points is equidistant from both the X and Y axes?

(-2, 2) (D), (3, -3) (E) Signup and view all the answers

Imagine a cube is sliced by a plane that passes through the midpoints of three edges that meet at one vertex. What is the shape of the cross-section created by the slice?

Equilateral triangle (A) Signup and view all the answers

If a line segment AB is rotated 90 degrees counterclockwise about point A, which statement accurately describes the relationship between the original line segment AB and the new line segment AB'?

The two line segments will be perpendicular. (B) Signup and view all the answers

Which of the following transformations would result in a figure that is congruent to the original figure?

Reflection across the X-axis (E) Signup and view all the answers

Given five different diagrams representing steps in folding a piece of paper and then making a single straight cut, which diagram represents the cut that will produce the most pieces of paper after unfolding?

diagram of pattern (A), diagram of pattern (B), diagram of pattern (C), diagram of pattern (D), diagram of pattern (E) Signup and view all the answers

A cylindrical object is viewed in perspective. Which statement best describes how parallel lines on the object's surface will appear in the perspective drawing?

Parallel lines will converge at a single vanishing point. (C) Signup and view all the answers

The Greenwich planetarium's roof is shaped like a truncated cone. If this cone is cut by two planes, $\alpha$ and $\beta$, where $\alpha$ is perpendicular to the cone's axis and $\beta$ is inclined, what shapes are created by these sections?

Circle; Ellipse (C) Signup and view all the answers

Masonry buildings typically have thicker walls on the ground floor compared to the upper floors. What is the primary reason for this design?

To better support progressively decreasing loads from the ground floor to the upper floors. (C) Signup and view all the answers

Imagine a cube. Which of the provided solid shapes can be added to solid (a) to perfectly form that cube?

Solid 2 (C) Signup and view all the answers

Identify the curvilinear shape that, when rotated, generates the surface of revolution depicted in the image.

Line design 1 (D) Signup and view all the answers

Among the following shapes, identify the two that are NOT identical to the other four.

Shapes 2 and 5 (D) Signup and view all the answers

Match the top-view floor plan with its corresponding front elevation drawing.

A (B) Signup and view all the answers

Which of the following correctly identifies five notable points within a triangle?

Centroid, incenter, circumcenter, orthocenter, and point of minimum distance from the vertices. (D) Signup and view all the answers

A lampshade's profile can be mathematically modeled as a truncated cone. If the equation defining the radius, $r$, at a height, $h$, is given by $r = 0.5h + 10$, what does the '0.5' represent in this equation?

The slope of the lampshade's side. (C) Signup and view all the answers

Which of the following pairings accurately matches the geometric shape view to its corresponding label?

1-E; 2-C; 3-B; 4-A; 5-D (C) Signup and view all the answers

Which of the following polyhedra, when appropriately sectioned by a plane, can generate all of these figures: rectangle, square, regular and irregular hexagon, pentagon, and triangle?

Cone (C) Signup and view all the answers

Given the photographic views of architectures and their corresponding plans, identify the series that correctly combines the plan and photographic view of each building.

Option A (A) Signup and view all the answers

Match the listed type of perspective to the corresponding graphic representation.

1-c; 2-b; 3-a (C) Signup and view all the answers

A sphere exposed to the sun cannot have one of the following portions in shadow. Which one?

Option A (E) Signup and view all the answers

The photo shows the Melancolía lamp by Santa & Cole (2005), inspired by Dürer's famous engraving from 1514, which proposes the geometry of a polyhedron. Which of the five numbered figures constitutes the correct geometric development of the lampshade?

Figure 1 (C) Signup and view all the answers

Determine the number of faces of the solid represented in the figure.

7 (A) Signup and view all the answers

To which representation of the metallic meter corresponds to figure A?

Option A (B) Signup and view all the answers

A diagram shows the inside of a building, specifically a church. What type of representation is depicted in the image?

An orthographic projection (A) Signup and view all the answers

The diagram shows the inside of a house with multiple floors. The representation can be best described as:

A section (A) Signup and view all the answers

Given a plane 'a' and a line 'r' perpendicular to 'a', which statement accurately describes the relationship between 'r' and the lines within plane 'a'?

'r' is orthogonal to all the lines of 'a' (E) Signup and view all the answers

Given a contour line representation showing points on a map, which of the options correctly schematizes the section A-A, which shows lines representing topography across a curve?

1 (D) Signup and view all the answers

Given different shapes and a diagram showing different shapes, match each preparatory drawing to its corresponding perspective projection.

1-A; 2-D; 3-B; 4-E; 5-C (E) Signup and view all the answers

Given the axonometric drawing of the STEL.MAN CHAIR by G.T. Rietveld, shown as a drawing of a chair, identify the correct corresponding pair of orthographic projections (front and side views).

1 (E) Signup and view all the answers

Match the correct sections from diagrams showing different shapes with sections denoted.

1-CC; 2-AA; 3-BB (E) Signup and view all the answers

Given the plan view of a church, which line of section corresponds to the section provided?

a-a' (E) Signup and view all the answers

Abbinare correttamente le figure in assonometria isometrica con le corrispondenti proiezioni ortogonali.

1 = c 2 = d 3 = a 4 = e 5 = b Signup and view all the answers

Quale delle seguenti affermazioni NON è corretta?

Un foglio di dimensioni A1 è pari a otto A4 (D) Signup and view all the answers

Facendo riferimento al piano che seziona l'insieme dei solidi, individuare la sezione in proiezione ortogonale corretta.

b (A) Signup and view all the answers

Date due viste di un cubo le cui facce hanno delle figure, individuare il corretto sviluppo.

2 (A) Signup and view all the answers

Stabilire la corretta corrispondenza tra i solidi di rivoluzione e le regioni plane rappresentati in figura.

1 = A 2 = D 3 = E 4 = C 5 = B Signup and view all the answers

Facendo riferimento al piano che seziona il gruppo di solidi dato (in pianta e prospetto), individuare la sezione corretta.

a (C) Signup and view all the answers

Data l'immagine tridimensionale di sedia, individuare la coppia di proiezioni ortogonali (vista frontale e vista laterale) esattamente corrispondenti.

e (E) Signup and view all the answers

Un cubo viene posto di fronte a due specchi posizionati perpendicolarmente l'uno rispetto all'altro, come mostrato in figura. Quale tra i seguenti cartoncini, una vorta piegato, consente di ottenere il cubo mostrato in figura?

2 (E) Signup and view all the answers

Dato un solido in proiezione ortogonale (pianta e prospetto laterale) individuare la esatta assonometria corrispondente.

b (D) Signup and view all the answers

Quale delle figure solide in basso, capovolta e unita a quella in alto, può ricostituire il cubo completo?

1 (D) Signup and view all the answers

Flashcards

Isometric vs. Orthographic Projections

Matching isometric views to their corresponding orthographic projections involves understanding how 3D shapes are represented in 2D from different viewpoints.

A-Series Paper Sizes

Paper sizes in the A series (A0, A1, A2, A3, A4) are related such that each size is half the area of the previous size. For example, A2 is half the size of A1.

A-size relationships

The A series is based on a logical halving of sizes, where each A(n) size is half the size of A(n-1). Thus, A0 is twice A1, four times A2, and so on.

Section in Orthographic Projection

A section in orthographic projection shows the shape created when a plane cuts through a 3D object, as viewed from a specific direction.