Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the number of edges, vertices, and faces of a triangular prism.
Edges:
Correct! A triangular prism has 9 edges, 6 vertices, and 5 faces.
(2) Name a polygon with 12 sides.
Perfect! A dodecagon has 12 sides and 12 vertices.
(3) Identify the 3D shape whose lateral surface is a rectangle and base is a circle.
Excellent! A cylinder has rectangular lateral surface and circular bases.
(4) Draw a cube and label its vertices as A, B, C...
Label vertices:
(5) Which 3D shape has all triangular faces?
Great! A tetrahedron (triangular pyramid) has 4 triangular faces.
Short Answer Questions (2 Marks Each)
Answer each question clearly
(1) A cylinder has a radius of 7 cm and height 10 cm. Name its lateral surface and total surface.
Lateral surface:
Total surface:
(2) Draw a hexagonal pyramid. Label the base and apex.
Base:
Apex:
Lateral faces:
(3) Identify the base, lateral faces, and vertices of a cuboid.
Bases:
Lateral faces:
Vertices:
(4) Draw a net for a triangular prism.
Net components:
(5) Draw a polygon with 8 sides and mark all its diagonals.
A regular
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete calculations and clear diagrams.
(1) A cone has a base radius of 5 cm and height 12 cm. Draw on the given below panel.
(2) Draw a cube with side 6 cm.
(3) Draw a cylinder with radius 4 cm and height 9 cm.
(4) Draw a square pyramid with base side 6 cm and height 8 cm.
(5) Draw lines of symmetry of a regular pentagon.
A regular pentagon has
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) A solid shape has 6 faces, all of which are rectangles. Which of the following must always be true?
(a) Opposite faces are equal and parallel
(b) All edges are equal
(c) All faces are squares
(d) It has exactly 6 vertices
Correct! The shape is a cuboid, not necessarily a cube.
(2) How many edges does a hexagonal prism have?
(a) 12 (b) 18 (c) 24 (d) 30
Correct! Hexagonal prism has 18 edges (6 + 6 + 6).
(3) The lateral surface of a cylinder is:
(a) Circular (b) Rectangular (c) Triangular (d) Hexagonal
Correct! When unfolded, a cylinder's lateral surface is rectangular.
(4) A pyramid has:
(a) One vertex at the top (b) Two vertices at the base (c) Three lateral faces (d) Four edges
Correct! All pyramids have exactly one vertex at the apex (top).
(5) A polygon with all sides equal and all angles equal is called:
(a) Regular (b) Irregular (c) Quadrilateral (d) Hexagon
Correct! A regular polygon has all sides and angles equal.
(6) Which of the following is not a prism?
(a) Triangular prism (b) Cube (c) Cylinder (d) Rectangular prism
Correct! A cylinder has curved surfaces, while prisms have only flat polygonal faces.
(7) Number of faces in a cube:
(a) 4 (b) 6 (c) 8 (d) 12
Correct! A cube has 6 square faces.
(8) A cone has:
(a) 2 vertices (b) 1 vertex (c) No vertex (d) 3 vertices
Correct! A cone has exactly 1 vertex at its apex.
(9) Which polygon has the maximum number of diagonals among these?
(a) Pentagon (b) Hexagon (c) Octagon (d) Heptagon
Correct! Octagon has 20 diagonals - the most among the given options.
(10) A pyramid has a square base and 4 triangular faces. How many edges and vertices does it have?
(a) 6 edges and 5 vertices
(b) 8 edges and 6 vertices
(c) 12 edges and 8 vertices
(d) 8 edges and 5 vertices
Correct! Square pyramid: 4 base edges + 4 slant edges = 8 edges, 4 base vertices + 1 apex = 5 vertices.
Expert Level 3D Shapes Challenge
Determine whether these statements are True or False:
Advanced 3D Shapes and Calculations Quiz
🎉 Congratulations! What You've Mastered:
You have successfully completed the "3D Shapes and Their Properties (Hard)" worksheet and learned:
(1) Advanced Shape Properties: Complex analysis of edges, vertices, and faces in sophisticated 3D shapes like hexagonal prisms and tetrahedrons
(2) Mathematical Calculations: Computing surface areas, volumes, and slant heights using precise formulas
(3) Polygon Mastery: Understanding complex polygons like dodecagons and calculating their diagonals systematically
(4) Surface Area Analysis: Distinguishing between lateral surface area, curved surface area, and total surface area
(5) Geometric Reasoning: Applying mathematical formulas to solve multi-step geometry problems
(6) Net Construction: Advanced visualization of how complex 3D shapes unfold into 2D nets
(7) Symmetry Properties: Analyzing lines of symmetry in regular polygons and geometric patterns
(8) Comparative Geometry: Understanding relationships between different classes of 3D shapes (prisms vs pyramids vs curved solids)
(9) Problem-Solving Expertise: Tackling challenging geometric problems requiring multiple steps and concepts
(10) Mathematical Communication: Using precise geometric terminology and expressing solutions with appropriate units
Outstanding achievement! You've conquered advanced 3D geometry with mathematical precision!