Moderate Level Worksheet Questions
Interactive Exploring Geometrical Figures Worksheet
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
Geometrical figures in 3D space include polyhedra, prisms, pyramids, and curved solids. Understanding their properties like faces, edges, vertices, and nets is essential for spatial reasoning and mathematical visualization.
First, let's explore basic 3D geometrical figures and their fundamental properties.
1. Define a polyhedron. Give one example.
Definition:
Example:
Perfect! A polyhedron is a 3D figure with flat faces, like a cube.
2. How many faces does a triangular prism have?
Excellent! A triangular prism has 2 triangular faces and 3 rectangular faces = 5 total.
3. Write the number of edges of a cube.
Great! A cube has 12 edges connecting its 8 vertices.
4. Name a 3D figure whose all faces are rectangles.
Correct! A cuboid (rectangular prism) has all rectangular faces.
5. What is the shape of the base of a cone?
Perfect! A cone has a circular base.
6. Define Euler's formula for polyhedra.
Excellent! Euler's formula: Faces + Vertices - Edges = 2.
7. Name a polyhedron that has 8 faces.
Great! An octahedron has 8 triangular faces.
8. How many vertices does a triangular pyramid have?
Perfect! A triangular pyramid (tetrahedron) has 4 vertices.
9. Is a sphere a polyhedron? Why?
Answer:
Reason: Because it has
Correct! A sphere is not a polyhedron because it has a curved surface, not flat faces.
10. How many flat faces does a cylinder have?
Excellent! A cylinder has 2 flat circular faces (top and bottom).
Drag each 3D shape to its correct category:
Part B: Short Answer Questions (2 Marks Each)
1. Draw a net of a cube and label its faces.
Step 1: How many faces does a cube have?
A cube net has
Step 2: What about the size?
All squares are
Perfect! A cube net consists of 6 equal squares that can fold into a cube.
2. A solid has 6 faces, 12 edges, and 8 vertices. Name the solid and verify Euler's formula.
Step 1: Identify the solid
With F=6, E=12, V=8, the solid is a
Step 2: Verify Euler's formula
F + V - E = 6 + 8 - 12 =
Excellent! It's a cube and Euler's formula is satisfied.
3. Name the type of prism with a pentagon as its base. How many edges does it have?
Step 1: Type of prism
Type of prism:
Step 2: Calculate edges
Pentagon has 5 sides, so prism has: 5 + 5 + 5 =
Great! A pentagonal prism has 15 edges (5 on top + 5 on bottom + 5 vertical).
4. How many faces, edges, and vertices does a square pyramid have? Verify Euler's formula.
Step 1: Count the parts
Faces =
Edges =
Vertices =
Step 2: Verify Euler's formula
F + V - E = 5 + 5 - 8 =
Perfect! Square pyramid: F=5, E=8, V=5, and Euler's formula holds.
5. Give two examples of solids that are not prisms.
Example 1:
Example 2:
Excellent examples! Pyramids and cones are not prisms.
Part C: Long Answer Questions (4 Marks Each)
1. Draw a neat net of a cylinder and explain how it forms the 3D figure when folded.
Step 1: Components of cylinder net
A cylinder net has
And
Step 2: Function of each part
The rectangle forms the
Circles form the
Perfect! When folded: rectangle wraps around to form curved surface, circles become top and bottom.
2. A polyhedron has 12 faces, 20 vertices, and 30 edges. Verify Euler's formula and name the solid.
Step 1: Verify Euler's formula
F + V - E = 12 + 20 - 30 =
Step 2: Identify the solid
This solid is an
Excellent! It's an icosahedron - a polyhedron with 20 triangular faces.
3. A prism has a hexagonal base. Find the total number of faces, edges, and vertices.
Step 1: Calculate faces
Number of faces = 2 bases + 6 rectangular faces =
Step 2: Calculate edges
Number of edges = 6 + 6 + 6 =
Step 3: Calculate vertices
Number of vertices = 6 + 6 =
Step 4: Verify Euler's formula
F + V - E = 8 + 12 - 18 =
Outstanding! Hexagonal prism: F=8, E=18, V=12.
4. Draw and explain the net of a square pyramid. How many triangles and squares does it have?
Step 1: Count triangular faces
Number of triangles =
Step 2: Count square faces
Number of squares =
Step 3: Total faces
Total faces = 4 + 1 =
Step 4: Base identification
The square forms the
Perfect! Square pyramid net: 4 triangles + 1 square base = 5 faces total.
5. Using Euler's formula, check whether a solid with 5 faces, 9 edges, and 6 vertices is possible.
Step 1: Apply Euler's formula
F + V - E = 5 + 6 - 9 =
Step 2: Conclusion
Since the result is 2, this solid is
Step 3: Identify the solid
This solid is a
Excellent! F=5, V=6, E=9 gives Euler's result of 2, so it's a valid triangular prism.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. The solid with all faces square is:
(a) Cube (b) Cuboid (c) Pyramid (d) Prism
Correct! A cube has all faces as equal squares.
2. Which of the following is not a polyhedron?
(a) Cube (b) Cone (c) Prism (d) Pyramid
Correct! A cone has a curved surface, so it's not a polyhedron.
3. A triangular prism has:
(a) 2 triangular faces and 3 rectangular faces (b) 2 triangular faces and 2 rectangular faces (c) 3 triangular faces and 2 rectangular faces (d) None of these
Correct! A triangular prism has 2 triangular bases and 3 rectangular faces.
4. Euler's formula for polyhedra is:
(a) F + E + V = 2 (b) F – E + V = 2 (c) F + E – V = 2 (d) F – E – V = 2
Correct! Euler's formula is F + V - E = 2 (or F - E + V = 2).
5. The number of edges in a hexagonal prism is:
(a) 12 (b) 18 (c) 20 (d) 24
Correct! Hexagonal prism: 6 + 6 + 6 = 18 edges (base + top + vertical).