Question

question 34 of 39
what shape is generated when rectangle abcd is rotated around the vertical line through a and d?
a. prism
b. cone
c. cylinder
d. pyramid

Explanation:

Step1: Recall 3 - D shapes formed by rotation

When a 2 - D shape is rotated around an axis, a 3 - D shape is formed.

Step2: Analyze rotation of a rectangle

A rectangle has two pairs of parallel sides. When rectangle \(ABCD\) is rotated around the vertical line through \(A\) and \(D\), the side \(AB\) (and \(CD\)) which is perpendicular to the axis of rotation (\(AD\)) will form a circular base. The height of the resulting 3 - D shape is the length of \(AD\).
A cylinder is defined as a solid figure with two circular bases and a curved surface. The rotation of the rectangle around the line \(AD\) (where \(AD\) is the height of the cylinder and \(AB\) is the radius of the circular bases) generates a cylinder.
A prism has two congruent polygonal bases (not necessarily circular). A cone is formed by rotating a right - triangle around one of its legs. A pyramid has a polygonal base and triangular faces. So the shape generated is a cylinder.

Answer:

C. Cylinder