Select the correct statements for the given figure.
(i) A hexagonal pyramid is placed with the axis perpendicular to V.P. and parallel to H.P.
(ii) The solid is kept with a pair of base edges parallel to V.P.
(iii) The solid is an example of solid of revolution.
(iv) The solid has total no. of seven surfaces.
Show Hint
To verify the number of surfaces ($S$) of any pyramid with a base of $n$ sides, use the simple formula: $S = n + 1$. For a hexagonal pyramid, $n = 6 \implies S = 7$.
Step 1: Analyzing the Given Isometric Projection of the Hexagonal Pyramid:
Let us evaluate each of the four statements given in the question:
• Statement (i): “A hexagonal pyramid is placed with the axis perpendicular to V.P. and parallel to H.P.”
Looking at the figure on Page 4, the axis of the hexagonal pyramid is directed vertically upwards. This means the axis is perpendicular to the Horizontal Plane (H.P.) and parallel to the Vertical Plane (V.P.). Thus, statement (i) is incorrect.
• Statement (ii): “The solid is kept with a pair of base edges parallel to V.P.”
Since the axis is vertical, the base of the pyramid lies on a horizontal plane. In the drawing, a pair of opposite edges of the hexagonal base is oriented horizontally (parallel to the XY line of projection representing the V.P.). Thus, statement (ii) is correct.
• Statement (iii): “The solid is an example of solid of revolution.”
Solids of revolution are formed by revolving a plane curve about an axis (e.g., cones, cylinders, spheres). A hexagonal pyramid is a polyhedron bounded by flat polygonal faces, not a solid of revolution. Thus, statement (iii) is incorrect.
• Statement (iv): “The solid has total no. of seven surfaces.”
A hexagonal pyramid consists of $1$ flat hexagonal base and $6$ flat triangular lateral faces, giving a total of $1 + 6 = 7$ surfaces. Thus, statement (iv) is correct.
Step 2: Combining the Results:
Since statements (ii) and (iv) are correct, option (C) is the correct answer.
