[Maths Class Notes] on Isometric Sketch Pdf for Exam

We can easily represent three-dimensional objects on a two-dimensional plane if the figures are drawn accurately. Representation of three-dimensional objects on a two-dimensional plane can be easily done using an oblique sketch. Although an oblique sketch is capable enough to draw the precise image of an object, sometimes the actual image of the object may vary when compared to the image drawn on a two-dimensional plane. To resolve this limitation, the isometric sketch is used to draw an object of the exact measurement along with the projection of its image on two dimensions.

Let us know more about an isometric sketch in detail

• The term isometric is derived from the Geek for “having equal measurement”. Hence, the isometric means having equal measurement or dimension.

• An image in an isometric sketch is drawn in such a way that the measurement of an original image remains the same regardless of its position.

Isometric Sketching Rules

Some of the isometric sketching rules are given below.

• As we know, an isometric object is usually drawn through vertical lines and horizontal lines. In isometric sketching, the vertical lines will remain vertical whereas the horizontal lines are formed at an angle of 30° to the horizontal plane.

• The angle between all the three axes of the coordinate plane should be equivalent to 120°.

• The isometric projection exhibits the three faces of an object, and all the three faces of an object are uniformly elongated.

Isometric Sketching Uses

• The isometric sketch is broadly used by engineers, designers, architects, infographics etc.

• Any object which is drawn with the help of the isometric projection exhibits an apparent visualization of the object.

• We can determine the accurate dimension of an object through isometric sketching.

• Isometric sketching can be used in situations when you have a clear picture of a product in your mind and you want to convey the product idea. You can convey your product idea through isometric sketching.

Isometric Sketching Example with Solutions

Below, you can see some of the isometric examples and solutions which will clear your concepts of isometric drawings.

The steps of an isometric sketching example of 8 × 3 × 3 cuboid are given below:

1. We can draw an isometric sketch of the cuboid with dimensions 8 × 3 × 3 using the isometric dot paper as given below.

2. The front side of the cuboid can be drawn by joining  8 dots which will form  the length of the cuboid and 3 adjacent dots which will form the breadth of the cuboid  as given below:

3. Draw 4 parallel lines from the corners of the rectangle drawn above in step 2.

4. Join the corner of the figure drawn above as shown in the figure given below.

5. On the basis of the convention, draw the hidden edges again as dotted lines as shown in the figure below:

Now, you can see the isometric sketching of a cuboid with dimension 8 × 3 ×3 in the figure below.

Hence, we can draw three-dimensional shapes of exact dimensions without any CO complexity with the help of an isometric dot paper.

1. Three cubes each with 3 cm is placed side by side to form a cuboid. Draw an isometric sketch of a cuboid and calculate the dimensions of the cuboid in cm.

Solution: Three cubes each with 3 cm is placed side by side to form a cuboid. 

Hence, the only one dimension of a cube will change whereas the other two dimensions will remain the same.

Out of three dimensions of cuboid, two dimensions of a cuboid will be 2 whereas the third dimension will be 2 + 2+ 2 = 6.

Hence, the dimension of cuboid will be 2*2*6.

Quiz Time

1. If an isometric projection is drawn with an accurate measurement but not with isometric scale the drawings are known as

1. Isometric projection

2. Isometric view

3. Isometric perception

4. Orthographic view

2. If an isometric drawing is formed with the use of isometric scale the the drawings are known as

1. Isometric projection

2. Isometric view

3. Isometric perception

4. Orthographic view

3. The angle formed between the isometric axes is

1. 180°

2. 60°

3. 90°

4. 120°