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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)
a cylinder
a sphere
a cone
a hemisphere
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A hemisphere.
Reason: Points on the quarter satisfy x^2 + y^2 = r^2 with x ≤ 0, y ≤ 0. Rotating about the x-axis gives x^2 + y^2 + z^2 = r^2 with x ≤ 0 — the half of a sphere (a hemisphere).
Reason: Points on the quarter satisfy x^2 + y^2 = r^2 with x ≤ 0, y ≤ 0. Rotating about the x-axis gives x^2 + y^2 + z^2 = r^2 with x ≤ 0 — the half of a sphere (a hemisphere).
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