Question

The region shown is revolved around the x-axis.





Question
What solid is the result of the revolution?

Answer options with 5 options
A.
cone

B.
cylinder

C.
pyramid

D.
sphere

E.
triangle

Answer 1

To determine the solid that results from revolving a region around the x-axis, we would typically need more information about the shape of the region being revolved. However, here’s a general guide based on common shapes:

- If the area being revolved resembles a line segment extending from the x-axis to a certain height (and has some defined linear boundaries), the result is generally a **cone** or **cylinder**.
- If it resembles two circular boundaries, it will typically result in a **cylinder**.
- A solid formed by revolving a triangle will generally result in a **cone**.
- If the shape resembles a sphere (like a circle being revolved), it will create a **sphere**.
- A triangle itself does not form a solid when revolved; it becomes a three-dimensional figure (usually a cone) instead.

Based on the options given:
- A **cone** could match if the region being revolved is triangular.
- A **cylinder** would be appropriate if the solid formed has flat ends.
- A **pyramid** is not the correct option since it does not result from a revolution around an axis.
- **Sphere** would only be the case if we are revolving a circular region.
- Lastly, **triangle** cannot be the result of revolution; it’s a shape.

Without the specific visual of the region, I’d recommend either "A. cone" or "B. cylinder" depending on whether the region forms a point to a base (cone) or has parallel sides (cylinder).

If you have further details about the region being revolved, please share, and I can give a more precise answer!