Question

quadrilateral abde is a rectangle. ab = 10 cm and ae = 16 cm. through which two points could a line of rotation be placed so that the base of the resulting cylinder will have a radius of 5 cm? d and e b and d c and f g and h

Explanation:

Step1: Recall the property of radius for cylinder - rotation.

When a rectangle is rotated about a line to form a cylinder, the distance from the line of rotation to the out - side of the rectangle becomes the radius of the base of the cylinder. Given \(AB = 10\mathrm{cm}\) and \(AE=16\mathrm{cm}\), if the radius of the base of the cylinder is \(5\mathrm{cm}\), the line of rotation should be placed at the mid - point of the side of length \(10\mathrm{cm}\).

Step2: Identify the mid - points.

Points \(G\) and \(H\) are the mid - points of the vertical sides of the rectangle \(ABDE\). When the rectangle is rotated about the line passing through \(G\) and \(H\), the radius of the base of the resulting cylinder is \(\frac{AB}{2}=\frac{10}{2}=5\mathrm{cm}\).

Answer:

G and H