GSEB Class 7 Maths Solutions Chapter 15 Visualising Solid Shapes Exercise 15.2

Question 1. Use isometric dot paper and make an isometric sketch for each one of the given shapes:
Answer: The task requires students to draw each of the given 3D shapes on isometric dot paper. This involves understanding how to represent depth and perspective accurately on a 2D surface. Below are the isometric sketches for the shapes provided in the question.
In simple words: Look at the shapes and draw them on special dotted paper so they look like real 3D objects.

Exam Tip: When drawing isometric sketches, remember that vertical lines stay vertical, and lines extending into depth are drawn at 30-degree angles to the horizontal. Consistency in angles and lengths is key for accuracy.

Question 2. The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Draw three different isometric sketches of this cuboid.
Answer: To draw three different isometric sketches, we can change which dimensions correspond to the length, width, and height visible from the front. This makes the cuboid appear to be rotated. Each sketch still accurately represents a 5x3x2 cm cuboid, but from a varied perspective.
In simple words: A cuboid has different sides. We draw it three ways, changing which side faces forward, but it's always the same size.

Exam Tip: When drawing isometric sketches, remember to use parallel lines for parallel edges and maintain consistent ratios for dimensions. Rotate the object mentally to achieve different views.

Question 3. Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.
Answer: When three cubes, each with a 2 cm edge, are placed next to each other, they form a cuboid with dimensions 6 cm (length), 2 cm (width), and 2 cm (height). The adjoining figure displays an isometric sketch of this combined cuboid.
In simple words: Three 2 cm cubes in a row make a cuboid that is 6 cm long, 2 cm wide, and 2 cm high. The drawing shows what it looks like.

Exam Tip: For composite shapes, calculate the total dimensions first. Then, draw the complete cuboid and add subtle lines to show the individual components, like the three cubes here.

Question 4. Make an oblique sketch for each one of the t given isometric shapes:
Answer: To create an oblique sketch, you typically use squared paper. The front face of the object is drawn true to size, while the receding edges are drawn at an angle (often 45 degrees) and usually at half their actual length to create a sense of depth. Since the specific isometric shapes were not provided in the question, an example of an oblique sketch of a simple cuboid is shown below to illustrate the technique.
In simple words: Draw the front of the shape normally on grid paper. Then, draw the sides going backwards at an angle, making them a bit shorter to show depth.

Exam Tip: For oblique sketches, always draw the front face accurately. The depth lines should be parallel and typically drawn at a 45-degree angle, often at half scale for a more natural appearance.

Question 5. Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:
(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)
(b) A cube with an edge 4 cm long. An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.
Answer: To create these sketches, you use different types of grid paper. For an oblique sketch, squared paper is used where the front face is accurate and depth is shown at an angle. For an isometric sketch, special dot paper helps represent all three dimensions in a way that shows depth equally. The solution states that the sketch of the cuboid is not unique, as you can draw it from various orientations.
In simple words: For oblique drawings, use square paper and show the front face clearly, then add slanted lines for depth. For isometric drawings, use special dotted paper to show all sides equally. No, your drawing of the cuboid isn't the only way to draw it, because you can turn it around.

(i) Oblique Sketch

(a) Cuboid of dimensions 5 cm, 3 cm and 2 cm:

(b) Cube with an edge 4 cm long:

(ii) Isometric Sketch

(a) Cuboid of dimensions 5 cm, 3 cm and 2 cm:

(b) Cube with an edge 4 cm long:

Exam Tip: Oblique sketches prioritize the true shape of one face, while isometric sketches aim for a balanced, three-dimensional view where all axes are equally foreshortened. Practice both techniques to improve your spatial visualization skills.