Question

Rotating a vertical strip between y = 8x³ and y = 8x around the x-axis creates a ________.

1) Cylinder
2) Cone
3) Sphere
4) Ellipsoid

Answer 1

Rotating a vertical strip between y = 8x³ and y = 8x around the x-axis creates a cone.

Step-by-step explanation:

Rotating a vertical strip between y = 8x³ and y = 8x around the x-axis creates a cone. When a vertical strip, which one can visualize as a line segment from the x-axis to the curve, is rotated around the x-axis, it will trace out a three-dimensional shape. In this instance, because we have y = 8x³ representing a cubic function and y = 8x representing a linear function, the shape formed is a cone, where the disparity in the radial distances from the x-axis at any given point creates a tapering form—as with a cone. This is also related to the concept of conic sections, where the intersection of a plane with a cone produces different shapes such as circles, ellipses, parabolas, and hyperbolas.