Visualising Solid Shapes: Important Questions and Answers for Class 8

Important Questions on Visualising Solid Shapes for Class 8 are available in this Maths article. Important Questions on Visualising Solid Shapes for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Visualising Solid Shapes. Visualising Solid Shapes covers 3D shapes, views from different sides, nets, and mapping space around us, which we use in everyday observations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• Exercise 1.1: Faces, Edges, and Vertices
• Exercise 1.2: Nets of Solid Shapes
• Exercise 1.3: Drawing 3D Shapes on a Flat Surface
• Exercise 1.4: Viewing Solids from Different Directions
• Tips for Understanding Visualising Solid Shapes for Class 8
• Most Common Examination Questions (Board Exams)

Exercise 1.1: Faces, Edges, and Vertices

Exercise 1.1.1: A cuboid has how many faces, edges, and vertices?

Answer: A cuboid has 6 faces, 12 edges, and 8 vertices. Think of a brick or a cereal box count the flat surfaces (6), the lines where surfaces meet (12), and the corners (8). You can verify this using Euler's formula: F + V - E = 2, so 6 + 8 - 12 = 2.

Exercise 1.1.2: Verify Euler's formula for a triangular prism.

Answer: A triangular prism has 5 faces (2 triangular + 3 rectangular), 9 edges, and 6 vertices. Applying Euler's formula: F + V - E = 5 + 6 - 9 = 2. The formula holds true.

Exercise 1.1.3: How many faces, edges, and vertices does a square pyramid have?

Answer: A square pyramid has 5 faces (1 square base + 4 triangular sides), 8 edges, and 5 vertices. Check: 5 + 5 - 8 = 2. Euler's formula is satisfied.

Exercise 1.1.4: Name a solid that has no vertex and no edge.

Answer: A sphere has no vertex and no edge. It has only one curved surface that wraps all the way around. Since it has no flat faces or corner points, Euler's formula does not apply to a sphere.

Exercise 1.2: Nets of Solid Shapes

Exercise 1.2.1: How many different nets can be drawn for a cube?

Answer: A cube has 11 different nets. Each net uses 6 squares arranged in different patterns that can fold into a cube. Not every arrangement of 6 squares forms a valid net for example, placing all 6 in a single row does not fold into a cube. It is a good idea to draw a few and try folding them mentally.

Exercise 1.2.2: Draw the net of a triangular prism and label its faces.

Answer: The net of a triangular prism consists of 2 triangles (the two end faces) and 3 rectangles (the three side faces). When you unfold the prism, the three rectangles lie in a row and the two triangles attach to the top and bottom of the middle rectangle. Label them: Triangle A (left end), Rectangle 1 (left side), Rectangle 2 (middle/bottom), Rectangle 3 (right side), Triangle B (right end).

Exercise 1.2.3: Which of these shapes does NOT have a net: sphere, cone, cube, cylinder?

Answer: A sphere does not have a net. A net is only possible for polyhedrons and shapes with flat or developable curved surfaces. A sphere has no flat face and its curved surface cannot be unrolled into a flat shape without distortion. Cones and cylinders have nets because their curved surfaces can be unrolled flat.

Exercise 1.2.4: Identify whether the given net can form a cube. (Net: T-shape of six squares.)

Answer: A T-shaped arrangement of six squares is not a valid net for a cube. When you try to fold it, one face overlaps another. A valid cube net must have six squares where no two faces will sit on the same position after folding. The correct approach is to check each fold step by step and see if any face is used twice.

Exercise 1.3: Drawing 3D Shapes on a Flat Surface

Exercise 1.3.1: What is the difference between an oblique sketch and an isometric sketch?

Answer: An oblique sketch shows the front face of the object as a true shape (exact dimensions), while the depth is drawn as diagonal lines that are shorter than actual size. It gives a quick 3D effect but is not perfectly proportional. An isometric sketch uses a special dotted grid where all lines are drawn at 30-degree angles and all dimensions are shown to scale, making the drawing more accurate and proportional. Isometric sketches are used in engineering and design work.

Exercise 1.3.2: Draw an oblique sketch of a cuboid measuring 4 cm x 3 cm x 2 cm.

Answer:

Step 1: Draw the front face as a rectangle 4 cm wide and 3 cm tall.

Step 2: From each corner of this rectangle, draw four parallel lines slanting at 45 degrees make these lines 1 cm long (half the actual depth of 2 cm).

Step 3: Connect the ends of these slanted lines to form the back face.

Step 4: The result is an oblique sketch of the cuboid.

Exercise 1.3.3: On isometric dot paper, draw a cube of side 3 units.

Answer:

Step 1: On the isometric dot paper, mark a starting dot.

Step 2: From this dot, draw three lines of equal length one going straight up, one going to the lower left at 30 degrees, and one going to the lower right at 30 degrees.

Step 3: Complete the three visible faces of the cube using parallelograms. Each face uses four equal-length lines.

Step 4: The cube should now show its top, left, and right faces clearly.

Exercise 1.3.4: In an oblique sketch, how is the depth of the solid shown?

Answer: In an oblique sketch, the depth of a solid is shown by drawing receding lines (also called oblique lines) at a 45-degree angle from each front face corner. These lines are drawn shorter than the actual depth of the object usually half the real depth to create the visual impression of three-dimensionality on a flat surface.

Exercise 1.4: Viewing Solids from Different Directions

Exercise 1.4.1: What will be the top view of a cone placed with its base on the ground?

Answer: When a cone is placed with its circular base on a flat surface and you look at it from directly above, you will see a circle with a dot in the centre. The outer circle represents the base of the cone, and the centre dot represents the apex (tip) of the cone. The top view of a cone is a circle.

Exercise 1.4.2: A solid is made of a cube topped with a square pyramid. What is its front view?

Answer: The front view of this solid (a cube topped with a square pyramid) would show a square at the bottom with a triangle sitting on top of it. The square represents the front face of the cube, and the triangle represents the front view of the pyramid sitting on top. Together, the shape looks like a house outline.

Exercise 1.4.3: What is the difference between the side view and the front view of a cylinder placed on its flat circular base?

Answer: When a cylinder stands upright on its circular base, both the front view and the side view look exactly the same they both appear as a rectangle. The width of the rectangle equals the diameter of the cylinder, and the height equals the height of the cylinder. This is because a cylinder looks the same from all sides around its curved surface.

Exercise 1.4.4: A building block has the following views: front view is a rectangle, side view is a rectangle, top view is a rectangle. What is the shape?

Answer: If all three views front, side, and top are rectangles, the solid is a cuboid (rectangular box). A cuboid's three pairs of opposite faces are all rectangles, so every direction shows a rectangular outline. If all three rectangles were squares of equal size, it would be a cube.

Tips for Understanding Visualising Solid Shapes for Class 8

• Use Real Objects Around You
• Memorise Euler's Formula
• Practise Drawing Nets by Hand
• Always Draw All Three Views
• Learn the Difference Between Oblique and Isometric Sketches
• Understand Cross-Sections
• Practise from Multiple Sources

Most Common Examination Questions (Board Exams)

1- Mark Questions

Q1. State Euler's formula for polyhedrons.

Solution: Euler's formula states that for any polyhedron, the number of Faces (F) plus the number of Vertices (V) minus the number of Edges (E) equals 2. Written as a formula: F + V - E = 2.

Q2. What is the top view of a sphere?

Solution: The top view of a sphere is a circle. No matter from which direction you look at a sphere, it always appears as a circle.

Q3. How many nets does a cube have?

Solution: A cube has exactly 11 different nets. Each net is a different arrangement of 6 squares that folds into a perfect cube.

Q4. What is a polyhedron?

Solution: A polyhedron is a solid shape whose all surfaces are flat (called faces). The faces meet at straight edges, and the edges meet at points called vertices. Examples include a cube, cuboid, pyramid, and prism. Shapes like spheres and cylinders are not polyhedrons because they have curved surfaces.

2 - Mark Questions

Q5. Verify Euler's formula for a tetrahedron.

Solution: A tetrahedron (triangular pyramid) has 4 faces, 4 vertices, and 6 edges. Applying Euler's formula: F + V - E = 4 + 4 - 6 = 2. The formula is verified.

Q6. A polyhedron has 6 faces and 8 vertices. How many edges does it have?

Solution: Using Euler's formula: F + V - E = 2. Substituting the values: 6 + 8 - E = 2. This gives 14 - E = 2, so E = 12. The polyhedron has 12 edges. This shape is a cuboid.

Q7. What does the front view of a cylinder lying on its curved surface look like?

Solution: When a cylinder lies on its curved surface (on its side), the front view shows a rectangle. The length of the rectangle equals the length (height) of the cylinder, and the width equals the diameter of the circular base.

Q8. Name the solid whose net consists of 1 circle and 1 sector of a circle.

Solution: The net that consists of one circle (the base) and one sector of a circle (the curved surface when unrolled) forms a cone. When the sector is rolled up and the circle is attached to its base edge, it becomes a cone.

3 - Mark Questions

Q9. Can a polyhedron have 10 faces, 20 edges, and 15 vertices? Explain using Euler's formula.

Solution: Step 1: Write Euler's formula: F + V - E = 2. Step 2: Substitute the given values: 10 + 15 - 20 = 5. Step 3: The result is 5, not 2. Step 4: Since the formula is not satisfied, such a polyhedron is not possible. Euler's formula must hold for any valid polyhedron.

Q10. Draw the front view, side view, and top view of a cube.

Solution: For a cube of side length s: Front view a square of side s. Side view a square of side s. Top view a square of side s. All three views of a cube are identical squares. This is because all six faces of a cube are equal squares and the cube looks the same from every direction.

Q11. Describe the cross-sections formed when a cone is cut by a plane in different ways.

Solution: Cutting a cone parallel to its base gives a circle. Cutting it parallel to one slant side (at an angle to the base) gives a parabola. Cutting it at an angle that passes through both sides of the cone gives an ellipse. Cutting it perpendicular to the base and through the apex gives a triangle (two triangles if cut all the way through). These shapes formed by cutting a cone are called conic sections.

Q12. Draw the net of a square pyramid and label all its faces. How many faces does the net have?

Solution: The net of a square pyramid consists of 5 faces in total: 1 square (the base) and 4 congruent triangles (the four slanting sides). To draw the net: place the square in the centre, then attach one triangle to each of its four sides, with the triangle tips pointing outward. When folded, the four triangles rise up and meet at the apex to form the pyramid. Label the central square as the base and each triangle as Face 1, Face 2, Face 3, and Face 4.