Question
A circle has its center at the origin of a coordinate plane. If you were to rotate that quarter about the x-axis, what three-dimensional object would be formed?(1 point) Responses a hemisphere a hemisphere a sphere a sphere a cylinder a cylinder a cone
Answers
GPT-4o mini
If you rotate a quarter (specifically, a quarter of a circle) about the x-axis, the three-dimensional object that would be formed is a **hemisphere**.
To clarify, when you have a quarter of a circle (say in the first quadrant), rotating it around the x-axis forms the upper half of a sphere. Since it covers all points from the origin to the radius along the x-axis and y-axis, it creates a half of the sphere that is entirely above the x-axis. Thus, the correct answer is **a hemisphere**.
To clarify, when you have a quarter of a circle (say in the first quadrant), rotating it around the x-axis forms the upper half of a sphere. Since it covers all points from the origin to the radius along the x-axis and y-axis, it creates a half of the sphere that is entirely above the x-axis. Thus, the correct answer is **a hemisphere**.