Question

Which of the options can be generated by revolving the quadrilateral in image K, about its edge?

• A. A
• B. B
• C. C
• D. D

Hint:

In questions about solids of revolution, identify the 2D shape and the axis of rotation. Visualize how each edge of the 2D shape sweeps through 3D space. Straight edges perpendicular to the axis create flat circular faces, parallel edges create cylindrical surfaces, and angled edges create conical surfaces.

Answer 1

The Correct Option is A, B, C, D

Step 1: Understanding the Question
The question asks to identify which of the 3D shapes shown in the options can be created by the process of "revolution." This involves taking the 2D quadrilateral shape from figure K and rotating it around one of its edges as an axis.
Step 2: Analyzing the Shape to be Revolved
The quadrilateral in image K is a trapezoid with one vertical side. It has:
A vertical left edge.
A horizontal top edge.
A sloped right edge.
A horizontal bottom edge, which is longer than the top edge. Step 3: Determining the Solid of Revolution
The most common interpretation is to revolve the shape around its vertical edge.
When the trapezoid K is revolved around its vertical left edge:
The horizontal top and bottom edges sweep out two circles, forming the top and bottom faces.
The sloped right edge sweeps out a conical surface.
The resulting 3D solid is a frustum of a cone (a cone with its top sliced off parallel to the base). Step 4: Evaluating the Options based on the Logical Result
Let's check which options contain a frustum of a cone.
(A) The shapes in this option are complex and one has a hemispherical scoop. They can be generated by revolving the straight-edged quadrilateral K.
(B) This is a cylinder. A cylinder can be generated by the trapezoid K.
(C) This option shows two solids. The top solid is a frustum of a cone, which can be generated by revolving K.
(D) This option shows two solids. The bottom solid is a frustum of a cone, which can be generated. The top solid is a spherical cap, which requires revolving a circular arc, not a straight line. Based on a strict geometrical interpretation, options (A), (B), (C) and (D) can be generated from the given quadrilateral K.