Isometric Projection

An isometric scale is used to measure true lengths along the isometric axes when drawing isometric projections. It helps in converting true lengths into isometric lengths, which are approximately 82% of the original lengths.
Steps to construct an isometric scale:
1. Draw a horizontal line and mark it as the true length line.
2. From the left end of this line, draw a line inclined at 45° — this line will represent true lengths.
3. From the same point, draw another line inclined at 30° — this will represent isometric lengths.
4. Mark regular intervals (e.g., 10 mm, 20 mm, 30 mm, etc.) on the 45° line.
5. From these marks, draw vertical lines to meet the 30° line.
6. The distances measured along the 30° line represent the isometric lengths.
Use: This scale is then used in isometric drawings to measure and draw isometric projections accurately.

The given figure shows a combination of two solids—a cone or pyramid and a sphere—arranged vertically.
Let us analyze each statement based on the geometry shown in the isometric view.
- Statement (i) is incorrect: The pyramid (or cone-like base) is clearly oriented vertically in the image, meaning its axis is not parallel to the H.P. (Horizontal Plane), but rather perpendicular to it. Thus, the claim that its axis is parallel to H.P. is wrong.
- Statement (ii) is correct: The upper part of the figure is a perfect circle in the isometric view, which indicates a sphere. Given that the figure also mentions a diameter of 70 mm, this confirms that a sphere of 70 mm diameter is placed on top of the base solid.
- Statement (iii) is correct: The vertical orientation of the pyramid implies its axis is perpendicular to H.P., which also means it is parallel to the V.P. (Vertical Plane). Furthermore, one of its base edges is visible aligned in such a way that it is perpendicular to the vertical plane, matching the statement accurately.
- Statement (iv) is incorrect: The base solid is not a prism—it’s a pyramid, and in any case, the axis is vertical, not perpendicular to V.P. The statement seems to confuse the geometry and orientation.
Hence, the correct pair of statements are (ii) and (iii).

The question requires identifying the isometric projection of a vertical square prism that is standing on top of a horizontal square slab.
Let’s break this down:
- A square slab is a short, thick block with a square base—its height is small relative to its length and breadth.
- A square prism is a tall 3D object with a square base and vertical sides—like a cube stretched vertically.
- When placed vertically on top of a slab, the overall object should look like a tall square prism mounted centrally over a shorter and wider square base.
Now evaluating the options: - Option (i) shows a stepped structure but does not represent a square prism on a slab—the base and top are not aligned vertically.
- Option (iii) shows the prism intersecting or merging with the base at the middle height—not placed over it.
- Option (iv) is close but lacks the proper proportions—the vertical prism does not appear distinct from the slab.
- Option (ii) clearly shows a vertical square prism standing above a larger, flat square slab. The shapes and orientation match the expected isometric view.
The base is horizontal and square, and the prism rises vertically and centrally from it, making it the correct representation.
Hence, the correct answer is (B) (ii).

We are asked to draw the isometric projection of a triangular prism with the following characteristics:
- Base edge = 35 mm
- Prism length (axis length) = 60 mm
- Placed on H.P. (Horizontal Plane) with one base edge
- Axis is perpendicular to V.P. (Vertical Plane)
Interpretation of orientation:
- Since the prism is placed on H.P., its triangular base lies flat on the horizontal plane.
- Axis perpendicular to V.P. means the prism faces the viewer head-on; one of its rectangular faces is parallel to the picture plane.
Construction steps:
1. Start by drawing the isometric axes at 30°, 90°, and 150°.
2. Construct the triangular base using isometric projection (base edge = 35 mm). Place it horizontally on the bottom face.
3. Project all three vertices upward using vertical lines to represent the length of the prism = 60 mm.
4. Join corresponding top points to complete the triangular prism.
5. Indicate the direction of viewing using a labeled arrow.
6. Apply dimensions using isometric dimensions — do not rotate text or dimension lines.
Dimensions to be shown:
- Base edge = 35 mm
- Prism height (axis length) = 60 mm
- Side edges and thickness lines of triangle
Label the drawing:
Title: Isometric Projection of a Triangular Prism (Scale 1:1)
Projection Type: Isometric Projection (using isometric scale from part a)