Question

each region below is being rotated about the line l. for each region, identify the solid generated by the rotation.

Explanation:

Step1: Recall rotation - solid relationships

When a right - angled trapezoid is rotated about a line parallel to its non - parallel side, a frustum of a cone and a cylinder combination is formed. When a right - angled triangle is rotated about one of its legs, a cone is formed.

Step2: Analyze region (a)

The region (a) is a trapezoid. When rotated about the line \(l\), it forms a solid that is a combination of a frustum of a cone and a cylinder.

Step3: Analyze region (b)

The region (b) is a right - angled triangle. When rotated about the line \(l\) (one of its legs), it forms a cone.

Step4: Analyze region (c)

The region (c) is a right - angled triangle. When rotated about the line \(l\) (parallel to one of its legs), it forms a cone.

Answer:

(a) A combination of a frustum of a cone and a cylinder
(b) A cone
(c) A cone