Question

select each shape that could be the two - dimensional cross - section of this cone.
a. circle
b. ellipse
c. right triangle
d. isosceles triangle

Explanation:

• A. Circle: A cross - section parallel to the base of the cone is a circle, as the base of the cone is a circle.
• B. Ellipse: A cross - section that is not parallel to the base and not passing through the vertex, at an angle, can be an ellipse.
• C. Right Triangle: A cross - section passing through the vertex and the center of the base (a vertical cross - section) of a right - circular cone is a right triangle. The height of the cone is perpendicular to the base radius, so the triangle formed has a right angle.
• D. Isosceles Triangle: Since the cone is a right - circular cone, the vertical cross - section (passing through the vertex and the base diameter) is an isosceles triangle. The two equal sides are the slant heights from the vertex to the ends of the base diameter.

Answer:

A. circle
B. ellipse
C. right triangle
D. isosceles triangle