Question

Select the correct option for the given isometric projection of combination of solids.

(i) The axis of pyramid is parallel to H.P. and one of its base edges is perpendicular to H.P.
(ii) A sphere of diameter 70 mm is placed on the top face of a prism.
(iii) The axis of pyramid is parallel to V.P. and one of its base edges is perpendicular to V.P.
(iv) The axis of prism is perpendicular to V.P. and one of its base edges is parallel to H.P.
 

• A. (iii) and (iv) only
• B. (iii) only
• C. (ii) and (iii) only
• D. (ii) only

Hint:

Always identify the axis direction to determine plane relations: vertical axis → perpendicular to H.P., parallel to V.P.

Answer 1

The Correct Option is C

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).