Question

what solid results when you rotate the shape around the segment \\(ab\\)?

a.
b.
c.
d.

Explanation:

Analyze the 2D shape and axis of rotation

The 2D shape is a regular pentagon.
The axis of rotation is the dashed line segment \(AB\).
Point \(A\) is a vertex of the pentagon.
Point \(B\) is the midpoint of the opposite horizontal base.

Determine the resulting 3D solid features

• The top vertex \(A\) lies on the axis of rotation, so rotating it creates a sharp point (cone-like apex) at the top.
• The two upper slanted sides meeting at \(A\) rotate to form a cone-like upper surface.
• The two lower nearly vertical sides rotate to form a curved, slightly tapered lateral surface.
• The bottom horizontal edge is perpendicular to the axis of rotation and meets it at its midpoint \(B\), forming a flat circular base.

Match with the given options

• Option A has a sharp pointed apex at the top and a flat circular base at the bottom, matching the rotation of a pentagon about its line of symmetry through a vertex.
• Option B has a flat top (frustum-like), which is incorrect.
• Option C is a frustum of a cone, which is incorrect.
• Option D has a flat top with an opening, which is incorrect.

Answer:

• (A) A solid with a sharp pointed top and a flat circular base (Correct answer)
• (B) A solid with a flat circular top and a flat circular base
• (C) A frustum of a cone
• (D) A rounded solid with flat circular openings at both ends