Question

through which points should a line of rotation be placed to create a cylinder with a radius of 3 units?
× e and j
○ f and i
○ j and g
○ g and e

Explanation:

Step1: Recall the formula for the radius of a cylinder formed by rotation

When a rectangle is rotated about a line to form a cylinder, the radius of the cylinder is the distance from the line of rotation to the side of the rectangle that forms the circular base of the cylinder.

Step2: Analyze each option

• Option E and J: If we rotate about the line through \(E\) and \(J\), the radius will be \(4\) units (the length of \(EF\) or \(GH\) perpendicular to \(EJ\)).
• Option F and I: The distance from the line through \(F\) and \(I\) to the side \(EG\) (or \(JH\)) is \(3\) units. When we rotate the rectangle about the line through \(F\) and \(I\), the radius of the resulting cylinder is \(3\) units.
• Option J and G: If we rotate about the line through \(J\) and \(G\), the radius is not a well - defined constant value for a circular base (since \(JG\) is a non - straight - line - parallel - to - the - required - rotation - axis in terms of creating a circular base with a single radius).
• Option G and E: If we rotate about the line through \(G\) and \(E\), the radius will be \(4\) units (the length of \(GH\) or \(EJ\) perpendicular to \(GE\)).

Answer:

F and I