Question

select the correct answer. a three - dimensional object is sliced perpendicular to its base. the result of the slice is a triangle. which figure could be the three - dimensional object? a. image of a cone b. image of a cylinder c. image of a rectangular prism d. image of a sphere

Explanation:

Step1: Analyze each option's cross - section

• For Option A (cone): When a cone is sliced perpendicular to its base, the cross - section is a triangle. The base of the cone is a circle, and a perpendicular slice from the apex to the base will form a triangular cross - section.
• For Option B (cylinder): A perpendicular slice to the base (which is a circle) of a cylinder will result in a rectangle (or a square if the cylinder has equal diameter and height in some cases), not a triangle.
• For Option C: The shape in Option C (the image shown) does not seem to be a shape where a perpendicular slice to its base would give a triangle.
• For Option D (sphere): A slice of a sphere, regardless of the direction (as long as it's a planar slice), will be a circle, not a triangle.

Step2: Determine the correct option

Based on the above analysis, the figure that when sliced perpendicular to its base gives a triangular cross - section is the cone (Option A).

Answer:

A. The cone (the figure labeled A)