How many practice questions are available for Visualising Solid Shapes?

SparkEd Math offers 60+ practice questions for Visualising Solid Shapes across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Visualising Solid Shapes content free on SparkEd Math?

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How does SparkEd Math teach Visualising Solid Shapes differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Visualising Solid Shapes problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Visualising Solid Shapes content aligned with the Olympiad syllabus?

Yes, all Visualising Solid Shapes questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Visualising Solid Shapes — Class 7 Olympiad (2025-26)

About Visualising Solid Shapes — Class 7 Olympiad

Identify 3D shapes from 2D representations, count faces/edges/vertices, and solve spatial reasoning puzzles. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 13). On this page you can practice 34 questions across three difficulty levels — 17 easy, 7 medium, and 10 hard — each with a visual step-by-step solution, plus a timed 17-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Visualising Solid Shapes — solved examples for Class 7 Olympiad

Example 1easy

A solid polyhedron has 10 faces and 16 edges. How many vertices does it have?

A)6
B)8
C)10
D)12

Step-by-step solution

Euler's formula states: V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces.
Given F = 10 and E = 16.
Substitute the values into the formula: V - 16 + 10 = 2.
Simplify: V - 6 = 2. Therefore, V = 2 + 6 = 8.

Answer: 8

Example 2medium

A cube is formed by folding the net shown below. Which pair of faces would be opposite to each other?

[Diagram description: A cross-shaped net for a cube.
Row 1: Empty box
Row 2: P | T | S
Row 3: Q | R | Empty box ]

A)P and R
B)T and S
C)Q and T
D)The empty box and P

Step-by-step solution

Let's label the positions on the net for clarity:
(Empty)
(P) (T) (S)
(Q) (R) (Empty)
By visualizing the fold, we can identify opposite pairs.
1. Faces 'P' and 'S' are opposite (separated by 'T' horizontally).
2. Faces 'T' and 'Q' are opposite (if 'T' is front, 'Q' folds up to be back).
3. The empty box at the top is opposite 'R' at the bottom.
Therefore, the pair Q and T are opposite faces.

Answer: Q and T

Example 3hard

A net is formed by 8 congruent equilateral triangles. When folded, it forms a regular octahedron. If each vertex of this octahedron is shared by exactly 4 edges, how many edges does the resulting octahedron have?

A)8
B)12
C)16
D)20

Step-by-step solution

A regular octahedron is a polyhedron with 8 faces (F=8), each an equilateral triangle. It is formed by joining two square pyramids at their bases.
We are given that each vertex of the octahedron is shared by exactly 4 edges. This means the degree of each vertex is 4. For any polyhedron, the sum of the degrees of all vertices is equal to twice the number of edges (2E = sum of vertex degrees).
Let V be the number of vertices and E be the number of edges. So, 2E = 4V. We also know F=8. Using Euler's formula for polyhedra (F+V-E=2): 8 + V - E = 2. From 2E = 4V, we get V = E/2. Substitute V into Euler's formula: 8 + (E/2) - E = 2.
Solving the equation: 8 - E/2 = 2 => E/2 = 6 => E = 12. Thus, a regular octahedron has 12 edges and 6 vertices (V=E/2=12/2=6). (Check: F+V-E = 8+6-12 = 2).

Answer: 12

Practice questions on Visualising Solid Shapes

Q1.easy
A solid is made of identical unit cubes. Its top view shows a 3×3 square grid with the center square missing. Its front view shows a 3×1 rectangle (3 cubes in a row). Which of the following could be its side view?
1. A)A 3×1 rectangle
2. B)A 2×1 rectangle
3. C)A 1×1 square
4. D)A 3×2 rectangle
Show answer
Answer: A 3×1 rectangle
Hint: First, determine the overall height of the solid from the front view. Then, combine this with the top view to deduce the side view.
Q2.easy
A solid has a pentagonal base and its lateral faces are triangles that meet at a single point (apex). What type of solid is this?
1. A)Pentagonal prism
2. B)Pentagonal pyramid
3. C)Cube
4. D)Cylinder
Show answer
Answer: Pentagonal pyramid
Hint: Consider the definitions of prisms and pyramids. How do their lateral faces and bases differ?
Q3.easy
Which of the following shapes CANNOT be a cross-section of a cuboid?
1. A)Triangle
2. B)Hexagon
3. C)Pentagon
4. D)Circle
Show answer
Answer: Circle
Hint: Think about the nature of the faces of a cuboid. What kind of edges will any cut produce?
Q4.medium
The top view of a 3D object is a square. The front view is a triangle. The side view (from the right) is also a triangle. Which of the following objects could it be?
1. A)A square pyramid
2. B)A cylinder
3. C)A cone
4. D)A triangular prism
Show answer
Answer: A square pyramid
Hint: Visualize each shape from different perspectives: looking down (top), looking from the front, and looking from the side.
Q5.medium
Which of the following 2D shapes *cannot* be a cross-section of a standard right circular cylinder?
1. A)Circle
2. B)Rectangle
3. C)Oval
4. D)Triangle
Show answer
Answer: Triangle
Hint: Consider all possible ways to slice a cylinder with a flat plane. Think about the nature of the cylinder's curved surface.
Q6.medium
A 3 × 3 × 3 cube is made up of 27 smaller unit cubes. If the entire large cube is painted blue on all its exterior faces, and then the unit cube at the very center (not visible from any side) is removed, how many faces of the *remaining* solid are painted blue?
1. A)54
2. B)48
3. C)42
4. D)36
Show answer
Answer: 54
Hint: Consider which parts of the large cube are painted. Does removing the very center cube affect the original exterior painted surfaces?
Q7.hard
A solid structure is built using 1×1×1 unit cubes. Its front view (looking from the front) shows a 2×2 square. Its top view (looking from above) shows 3 cubes in an 'L' shape: [ (1,1) ; (1,2) (2,2) ] (where (x,y) are grid coordinates). Its side view (from the right) shows 3 cubes in an 'L' shape: [ (1,2) ; (1,1) (2,1) ] (where (y,z) are grid coordinates). What is the minimum number of cubes required to build this structure?
1. A)4
2. B)5
3. C)6
4. D)7
Show answer
Answer: 5
Hint: Systematically analyze the implications of each view on a 2x2x2 grid. Identify cells that must be empty and then fill the minimum necessary cells to satisfy all visible projections.
Q8.hard
A specific 3D solid, when cut by a single plane, can produce a regular hexagon as its cross-section. Which of the following solids CANNOT produce a regular hexagon cross-section?
1. A)A Cube
2. B)A Regular Octahedron
3. C)A Regular Tetrahedron
4. D)A Regular Hexagonal Prism
Show answer
Answer: A Regular Tetrahedron
Hint: Consider the maximum number of faces a plane can intersect in each solid. A hexagon requires intersection with at least six faces.
Q9.hard
A cube and a square pyramid (with its base congruent to one face of the cube) are joined by gluing their congruent bases together. What is the sum of faces, edges, and vertices (F+E+V) of the resulting composite solid?
1. A)32
2. B)30
3. C)36
4. D)34
Show answer
Answer: 34
Hint: When two solids are joined, count the individual faces, edges, and vertices, then subtract any that become internal (shared) after joining.

These are 9 of the 34 questions available for Visualising Solid Shapes. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.