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Visualising Solid Shapes introduces students to various dimensions and properties of geometrical figures like cubes, cuboids, spheres, cylinders, and cones. It includes many new concepts like Euler’s Formula, prisms, polyhedrons, faces, edges, vertices, and mapping space around us. Visualising Solid Shapes is about learning how different solid figures look when they are viewed from different dimensions.
Ques 1. What is the name of the shape given alongside?
- Cube
- Rectangle
- Cuboid
- Square
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Answer: A
Explanation: A three-dimensional solid figure having 6 equal sides that are squares is called a cube.
Ques 2. What does the top view of a cube look like?
- Rectangle
- Square
- Circle
- Triangle
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Answer: B
Explanation: A cube has 6 faces with equal lengths, making it a square. Thus, the top view of a cube looks like a square.
Ques 3. What is the name of the figure given alongside?
- Square
- Cuboid
- Rectangle
- Cube
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Answer: B
Explanation: A three-dimensional solid figure with 6 faces that are rectangular in shape is called a cuboid. A cuboid has three parameters- length, breadth, and height.
Ques 4. What does the top-view of a cuboid look like?
- Triangle
- Square
- Circle
- Rectangle
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Answer: D
Explanation: A cuboid is a three-dimensional geometrical figure with rectangular faces having opposite sides as equal. Thus, the top-view of a cuboid looks like a rectangle.
Ques 5. What is the name of this figure?
- Triangle
- Sphere
- Cone
- Cube
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Answer: C
Explanation: the given figure is called a cone as it has a pointed top and sides that form a circular shape at the bottom. Example: an ice cream cone.
Ques 6. Which of the following is an example of a cone?
- Tent
- Glass
- Ball
- Bottle
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Answer: A
Explanation: A cone is a three-dimensional geometrical figure that has a pointed top and sides that form a circular shape at the bottom (a three-dimensional version of a triangle). Thus, out of the given options, Tent is an example of a cone.
Ques 7. What does the top view of a cone look like?
- Triangle
- Circle
- Rectangle
- Square
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Answer: B
Explanation: Cone is a geometric figure with a circular base. Therefore, when viewed from the top, it looks like a circle with its vertex as the center of the circle.
Ques 8. Which of the following is an example of a cylinder?
- Box
- Pipe
- Scale
- Book
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Answer: B
Explanation: A cylinder is a geometrical figure that has two parallel circular bases opposite each other joined by a curved surface, at a fixed distance from the center. Example: pipes, cans, LPG cylinders, etc.
Ques 9. How many sides does a sphere have?
- Six
- Eight
- Four
- None
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Answer: D
Explanation: A sphere is a three-dimensional geometric object that is circular in shape, thus having no sides, corners, or edges.
Ques 10. How many faces does a cuboid have?
- Two
- Four
- Six
- Eight
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Answer: C
Explanation: A three-dimensional solid figure with 6 faces that are rectangular in shape is called a cuboid. A cuboid has three parameters- length, breadth, and height.
Ques 11. A cube is a three-dimensional solid figure. Choose if the given statement is True or False.
- True
- False
- Both
- None
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Answer: A
Explanation: The given statement is true as the cube is a three-dimensional figure with 6 square faces, 8 vertices, and 12 edges.
Ques 12. What is the shape of the base of a prism?
- Triangle
- Circle
- Rectangle
- Any of the above
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Answer: D
Explanation: A prism is a three-dimensional object with two identical ends. The faces of a prism are usually parallelograms or rectangles, but the bases of the prism could be a square, a triangle, or any polygon.
Ques 13. Prisms and Pyramids are:
- Polyhedrons
- Cubes
- Cuboids
- Spheres
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Answer: A
Explanation: A polyhedron is a three-dimensional geometrical shape that has flat polygonal faces, straight edges, and sharp corners. Prisms and pyramids both contain sides and faces that are polygons, with straight edges and corners, thus making them a polyhedron.
Ques 14. If a polyhedron has 6 vertices and 12 edges. How many faces does it have?
- 2
- 4
- 6
- 8
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Answer: D
Explanation: By Euler’s formula we know that:
For any polyhedron,
F + V – E = 2
F = 2 – V + E
F = 2 – 6 + 12
Thus, F = 8 i.e., the number of faces.
Ques 15. “A square is a two-dimensional figure”. Choose the correct alternative for the given statement.
- True
- False
- Both A and B
- None of the above
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Answer: A
Explanation: The given statement is true as a square is a two-dimensional figure having all sides equal.
Ques 16. How many faces does a triangular prism have?
- 6
- 3
- 5
- 8
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Answer: C
Explanation: A triangular prism is a three-dimensional figure that is made up of two triangular bases and three rectangular sides, thus making it a total of 5 faces.
Ques 17. If F, E, and V represent the faces, edges, and vertices respectively of a polyhedron, then which of the following is the correct Euler’s formula?
- F – V + E = 2
- F + V – E = 2
- F + V = – 2
- F + V + E = 2
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Answer: B
Explanation: If F, E, and V represent the faces, edges, and vertices respectively of a polyhedron, then we get F + V – E = 2 as the Euler’s Formula.
Ques 18. 3D objects have the same views from different positions. Choose the correct alternative for the given statement.
- True
- False
- Both True and False
- None of the Above
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Answer: B
Explanation: Three-dimensional objects have different views from different positions. They are solid figures and thus can be viewed through different angles resulting in a different view from every different position.
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