CBSE Class 7 Mathematics Visualising Solid Shapes Assignment

Question 1. Draw the nets of a cube , cuboid & cylinder.
Answer:
- Net of a cube: Consists of 6 identical square faces arranged in a cross or T-shape.
- Net of a cylinder: Consists of two identical circles (top and bottom bases) and one rectangle (curved surface area).
- Net of a cuboid: Consists of 6 rectangular regions joined together.
In simple words: Nets are 2D flat patterns that can be folded to make 3D shapes.

Exam Tip: Practice drawing the standard 6-square cross net for cubes and the rectangle-plus-two-circles net for cylinders.

Question 2. A line where two faces of a solid meet is called its ----------------.
Answer: Edge.
In simple words: An edge is the straight line segment where two flat surfaces meet.

Exam Tip: Remember that edges form the skeleton framework of a solid shape.

Question 3. A cylinder has ---------faces , ---------vertices & -------------edges.
Answer: A cylinder has 3 faces (2 flat circular faces and 1 curved face), 0 vertices, and 2 curved edges.
In simple words: A cylinder has no sharp corners (vertices), two circular rims (edges), and three surfaces.

Exam Tip: Do not confuse flat faces with curved faces when counting.

Question 4. A cube has ---------faces , ---------vertices & -------------edges.
Answer: A cube has 6 faces, 8 vertices, and 12 edges.
In simple words: A standard box shape always has 6 flat square faces, 8 corners, and 12 straight edges.

Exam Tip: Use Euler's formula \(F + V - E = 2\) to verify: \(6 + 8 - 12 = 2\).

Question 5. The corner where three faces of a solid meet is called its -------------.
Answer: Vertex (or corner).
In simple words: A vertex is a point where multiple edges and faces intersect.

Question 6. All solid figure have -----------dimensions.
Answer: 3 (Three dimensions: length, breadth, and height/depth).
In simple words: Solids occupy space and therefore have three dimensions.
Exam Tip: 2D shapes have length and breadth only, while 3D shapes add thickness or height.

Question 7. The flat surface of a solid are called its -------------.
Answer: Faces.
In simple words: The flat sides of a 3D object are its faces.

Exam Tip: Spheres and cylinders have curved surfaces, but polyhedra have flat faces.

Question 8. A pyramid is a -----------dimensional figure.
Answer: 3 (Three-dimensional).
In simple words: A pyramid is a solid object that has height, width, and depth.

Exam Tip: Pyramids have a flat base and triangular faces that meet at a common top vertex.

Question 9. A tetrahedron is also named as a -------------------.
Answer: Triangular pyramid.
In simple words: A tetrahedron is a pyramid with a triangular base, giving it a total of 4 triangular faces.

Exam Tip: Remember that "tetra" means four, so a tetrahedron has 4 faces.

Question 10. A rectangular prism is also called a --------------.
Answer: Cuboid.
In simple words: A box with rectangular faces is mathematically called a rectangular prism or cuboid.

Exam Tip: A cube is a special type of rectangular prism where all lengths, breadths, and heights are equal.

Question 11. Which of these nets matches with that of a cone ?
Answer: Net (d) [referring to the circular base attached to a sector of a circle].
In simple words: A cone net consists of a circular base and a sector of a circle (pie slice shape) for the curved lateral surface.

Exam Tip: A cone's lateral net is not a triangle; it is a circular sector.

Question 12. What cross - section do you get when you give a (i) vertical cut (ii) horizontal cut to the following solids ?
(a) A brick (b) A round apple (c) A die (d) A circular pipe (e) An ice cream cone (f) A joker cap
Answer:
(a) A brick: (i) Vertical cut: Rectangle | (ii) Horizontal cut: Rectangle
(b) A round apple: (i) Vertical cut: Circle / Oval | (ii) Horizontal cut: Circle
(c) A die: (i) Vertical cut: Square | (ii) Horizontal cut: Square
(d) A circular pipe: (i) Vertical cut: Rectangle | (ii) Horizontal cut: Circle (Ring/Annulus)
(e) An ice cream cone: (i) Vertical cut: Triangle | (ii) Horizontal cut: Circle
(f) A joker cap: (i) Vertical cut: Triangle | (ii) Horizontal cut: Circle
In simple words: A cross-section is the face you see when you slice straight through an object.

Exam Tip: Visualize slicing a loaf of bread or fruit to easily determine cross-sectional shapes.

Question 13. A bulb is kept burning just right above the following solid. Name the shape of the shadows obtained in each case .Attempt to give a rough sketch of the shadow.
(a) A brick (b) A round apple (c) A die (d) A circular pipe (e) An ice cream cone (f) A joker's cap (g) A ball
Answer:
(a) A brick: Rectangle shadow.
(b) A round apple: Circular shadow.
(c) A die: Square shadow.
(d) A circular pipe: Rectangular shadow (if viewed from side) or Circular ring shadow (if viewed from top).
(e) An ice cream cone: Triangular shadow.
(f) A joker's cap: Triangular shadow.
(g) A ball: Circular shadow.
In simple words: Shadows show the 2D silhouette of a 3D object when light is shone directly onto it.

Exam Tip: Parallel light rays cast exact shadow shapes corresponding to the facing profile of the object.

Question 14. The dimensions of a cuboid are \(5\text{ cm}\), \(3\text{ cm}\) & \(2\text{ cm}\) . Draw three different isometric sketches of this cuboid .
Answer:
To draw isometric sketches, use isometric dot paper or 30-degree inclined axes.
1. Sketch 1: Length \(5\text{ cm}\) along the right axis, breadth \(3\text{ cm}\) along the left axis, and height \(2\text{ cm}\) vertically.
2. Sketch 2: Length \(3\text{ cm}\) along the right axis, breadth \(5\text{ cm}\) along the left axis, and height \(2\text{ cm}\) vertically.
3. Sketch 3: Length \(2\text{ cm}\) along the right axis, breadth \(5\text{ cm}\) along the left axis, and height \(3\text{ cm}\) vertically (varying orientation).
In simple words: Isometric sketches show 3D objects on 2D paper using 30-degree angle guidelines.

Exam Tip: Always use a sharp pencil and ruler for isometric drawings.

Question 15. Three cubes each with \(2\text{ cm}\) edge are placed side by side to form a cuboid . Sketch an oblique & isometric sketch of this cuboid .
Answer:
- Dimensions of the resulting cuboid: Length = \(2 + 2 + 2 = 6\text{ cm}\), Breadth = \(2\text{ cm}\), Height = \(2\text{ cm}\).
- Oblique sketch: Draw a front face of dimensions \(6\text{ cm} \times 2\text{ cm}\), draw receding lines at \(45^{\circ}\) of length \(2\text{ cm}\), and complete the back rectangular face.
- Isometric sketch: Draw on isometric dot sheets with length \(6\text{ cm}\) (3 units), breadth \(2\text{ cm}\) (1 unit), and height \(2\text{ cm}\) (1 unit).
In simple words: Joining three identical cubes end-to-end forms a long cuboid where only the length increases.

Exam Tip: Double-check the total dimensions before sketching combined shapes.