Question

question 5(multiple choice worth 1 points)
(06 - 04 mc)
around which line would the following cross - section need to be revolved to create a sphere?
ox - axis
oy = x
ox = 1
oy = 1

Explanation:

Step1: Recall the property of a sphere

A sphere is symmetric in all directions. When a circle (cross - section) is revolved around a line such that the distance from every point on the circle to the line of revolution is the same.

Step2: Analyze the center of the circle

The center of the given circle has coordinates \((x = 1,y = 9)\). If we revolve the circle around the line \(x = 1\), the distance from every point on the circle to the line \(x=1\) (using the formula \(d=\vert x - x_0\vert\) for a vertical line \(x = x_0\)) is the horizontal distance from the point \((x,y)\) on the circle to the line \(x = 1\). Since the line \(x = 1\) passes through the center of the circle, for any point \((x,y)\) on the circle, the distance \(d=\vert x - 1\vert\) (for a vertical line \(x = 1\)) is the radius of the circle.

Answer:

\(x = 1\)