Q1: Which of the following is NOT a characteristic of solid shapes? (a) They have length, width, and height (b) They occupy space and have volume (c) They are flat with no thickness (d) They are three-dimensional shapes
Solution:
Ans: (c) Solid shapes are three-dimensional objects with length, width, and height. They occupy space and have volume, unlike flat plane figures which have no thickness.
Q2: What is a net in the context of 3D shapes? (a) A fishing tool used in geometry (b) A two-dimensional skeleton outline that can be folded to form a 3D shape (c) A three-dimensional model of a shape (d) A type of solid shape with circular faces
Solution:
Ans: (b) A net is a flat, two-dimensional skeleton outline which, when folded and joined with glue, creates a three-dimensional shape like a cube or cylinder.
Q3: How many faces does a cube have? (a) 4 (b) 8 (c) 12 (d) 6
Solution:
Ans: (d) A cube has six flat surfaces or faces. Each face is a square, and these faces make up the complete surface of the cube.
Q4: Which method of drawing 3D shapes involves using special isometric sheets and taking measurements? (a) Isometric sketches (b) Oblique sketches (c) Shadow casting (d) Net drawing
Solution:
Ans: (a) Isometric sketches are drawn on special isometric sheets and involve taking measurements of the 3D object, unlike oblique sketches which are drawn by hand without tools.
Q5: What are vertices in a 3D shape? (a) The flat surfaces of the shape (b) The line segments joining two faces (c) Points where two or more edges meet between faces (d) The shadows cast by the shape
Solution:
Ans: (c) Vertices are the corners of a 3D shape where two or more edges meet between faces. For example, a cube has eight vertices at its corners.
Fill in the Blanks
Q1: A 2D image has only two dimensions: length and _____.
Solution:
Ans: width
Q2: Solid shapes are also known as _____ shapes.
Solution:
Ans: three-dimensional
Q3: The flat surface of a 3D shape is called a _____.
Solution:
Ans: face
Q4: _____ are the line segments which join one vertex to another vertex.
Solution:
Ans: Edges
Q5: A cube has _____ vertices.
Solution:
Ans: 8
True or False
Q1: Plane figures are three-dimensional shapes that occupy space.
Solution:
Ans: False Plane figures are flat or two-dimensional figures with no thickness, such as squares, rectangles, circles, and triangles.
Q2: A cylinder has 2 edges.
Solution:
Ans: True A cylinder has exactly two edges, which are the circular boundaries where the curved surface meets the flat circular faces.
Q3: Oblique sketches involve measuring the actual size of the 3D object.
Solution:
Ans: False Oblique sketches are drawn by hand without using tools and do not involve measuring the actual size of the 3D object.
Q4: Shadow casting creates a two-dimensional representation of a three-dimensional object.
Solution:
Ans: True Shadow casting is a technique that creates a two-dimensional representation by casting the shadow of a three-dimensional object onto a surface.
Q5: Solid shapes have only length and width but no height.
Solution:
Ans: False Solid shapes are three-dimensional and have three dimensions: length, width, and height, unlike two-dimensional plane figures.
Match the Following
Column A
Column B
1. Two-dimensional shapes with no thickness
A. Eight
2. Number of vertices in a cube
B. Isometric sheets
3. Line segments joining vertices
C. Edges
4. Special sheets used for isometric sketches
D. Plane figures
5. Number of faces in a cube
E. Six
Solution:
Ans:
1 - D: Plane figures are flat, two-dimensional shapes with no thickness, such as squares, rectangles, circles, and triangles.
2 - A: A cube has eight vertices, which are the corner points where three edges meet together.
3 - C: Edges are the line segments that join one vertex to another vertex in a three-dimensional shape.
4 - B: Isometric sketches are drawn on special sheets called isometric sheets, which help in creating accurate three-dimensional drawings.
5 - E: A cube has six flat surfaces or faces, with each face being a square of equal size.
Short Answer Questions
Q1: What is the difference between 2D and 3D images?
Solution:
Ans: A 2D image is like a flat drawing with only two dimensions: length and width, appearing on a flat surface like paper. A 3D image represents the real object with three dimensions: length, width, and height. 3D shapes have depth and occupy space, making them more realistic than flat 2D shapes.
Q2: Explain what faces, edges, and vertices are in 3D shapes.
Solution:
Ans:
Faces are the flat surfaces of a 3D shape, such as the six faces of a cube.
Edges are line segments joining one vertex to another, like the twelve edges of a cube.
Vertices are corner points where two or more edges meet, such as the eight vertices in a cube.
Q3: What is a net and how is it used to create 3D shapes?
Solution:
Ans: A net is a two-dimensional skeleton outline of a three-dimensional shape. It is a flat pattern that, when folded and joined together with glue, forms a 3D shape. Nets are basic outlines that help visualise how flat surfaces combine to create solid shapes like cubes and cylinders.
Q4: Describe two methods of drawing solid shapes on a flat surface.
Solution:
Ans:
Oblique sketches show 3D objects from different angles, drawn by hand without tools and without measuring actual sizes.
Isometric sketches involve both drawing and taking measurements, created on special isometric sheets to accurately represent three-dimensional objects with proper proportions and dimensions.
Q5: How does shadow casting help in viewing different sections of a solid?
Solution:
Ans: Shadow casting creates a two-dimensional representation of a three-dimensional object by casting its shadow. The resultant shape depends on the side from which light is thrown. For example, light on a cylinder's circular side creates a circular shadow, whilst light on its standing position creates a rectangular shadow.
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