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 an isosceles trapezoid. The axis of rotation is the segment \(AB\), which is the line of symmetry passing perpendicularly through the top and bottom parallel bases of the trapezoid.

Determine the resulting 3D solid

Rotating a trapezoid about its line of symmetry of the bases sweeps out a truncated cone, also known as a frustum of a cone. The top base sweeps out a smaller circular flat top, the bottom base sweeps out a larger circular flat bottom, and the slanted sides sweep out a conical surface.

Match with the given options

• Option A represents a cone combined with a frustum.
• Option B represents a double frustum.
• Option C represents a single frustum of a cone (a truncated cone with a flat top and a flat bottom).
• Option D represents an ellipsoid.

Therefore, the correct solid is represented by Option C.

Answer:

• (A) cone on top of a frustum
• (B) double frustum
• (C) frustum of a cone (Correct answer)
• (D) ellipsoid