Question

rotating a rectangle
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 rotating a rectangle

When a rectangle is rotated about a line, the radius of the resulting 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 the rectangle about the line through \(E\) and \(J\), the radius of the resulting cylinder will be the length of \(EF\) or \(FG\) (since the side perpendicular to the line of rotation \(EJ\) will form the circular base). The length \(EF = 3\) units.
• Option F and I: If we rotate about the line through \(F\) and \(I\), the radius is not \(3\) units. The distance from the line \(FI\) to the adjacent sides is not \(3\) (by visual inspection of the rectangle's side - lengths \(EJ = 4\), \(EF=3\)).
• Option J and G: If we rotate about the line through \(J\) and \(G\), the radius is not \(3\) units. The distance from the line \(JG\) to the adjacent sides is not \(3\) (using the properties of the rectangle \(EJ = 4\), \(EF = 3\)).
• Option G and E: If we rotate about the line through \(G\) and \(E\), the radius is not \(3\) units. The distance from the line \(GE\) to the adjacent sides is not \(3\) (using the side - lengths of the rectangle \(EJ=4\), \(EF = 3\)).

Answer:

E and J