A circle has its center at the origin of a coordinate plane. If you were to isolate one-quarter of the circle in Quadrant III and rotate that quarter about the x-axis, what three-dimensional object would be formed? (1 point)

Question

• a cylinder
• a sphere
• a cone
• a hemisphere

Answer 1

When you take one-quarter of a circle in Quadrant III and rotate it about the x-axis, you create a three-dimensional object.

The quarter circle in Quadrant III includes points where \(x\) is negative and \(y\) is negative, forming a quarter of a circle that looks like a "slice" of the circle in that quadrant. When this quarter circle is rotated about the x-axis, it sweeps out a three-dimensional shape.

The shape that is formed by this rotation is a hemisphere. This is because the rotation creates a half-sphere (or hemisphere), as the circular shape is revolved around the x-axis.

Therefore, the correct answer is:

• a hemisphere