Question

What is the shape of the cross section of the cone in each situation?

Answer 1

First case: that's definitely a circle.
Second case: if you have a cross section / plane perpendicular to the base and passing thru the vertex, you have a triangle. Try drawing this.

Answer 2

When the cone is sliced parallel to the base we obtain--

Circle.

and when the cone is sliced perpendicular to the vase and passes through the vertex we get--

Triangle.

Explanation:

• We know that when a three dimensional figure is sliced parallel to it's base then the cross-section so obtained is similar to the base of the figure.

As we know that the base of a cone is in the shape of a circle.

Hence, the cross-section so obtained is a circle.

• Similarly when we slice a cone perpendicular to base then we obtain a figure similar to it's face.

Hence, in the case of cone when the slicing is done perpendicular to the base and passes through it's vertex then we obtain:

Triangle.