Question

Which shape could not be the intersection of a cone and a plane?

Answer 1

Question 1

An ellipse, circle and parabola are all possible figures we can make if we intersect a plane and a cone. These are called conic sections. 

A rectangle is NOT a conic section and not possible to form it with an intersection of a cone and a plane.

Answer: Choice A) rectangle

=============================================

Question 2

The shaded cross section is a parabola. It stretches onward forever as you move down the bottom cone. This plane won't intersect the top cone at all.

=============================================

Question 3

Spinning the rectangle around that line will create a flattened cylinder, which is what choice A is showing. Think of a fan blade spinning really fast, or a revolving door. 

=============================================

Question 4

A pentagonal pyramid has a pentagonal cross section. So that rules out choice A.

A cylinder could have a rectangular cross section if the plane is perpendicular to the base. 

Choice C is eliminated since we can only form triangles or circles as cross sections here.

A tetrahedron could have a square cross section, which is a special case of a rectangle, making choice D a possibility as well.

So the answer is either choice B or choice D. If your teacher is excluding squares, then we can eliminate choice D making B as the only answer. Though I'm not 100% sure on this one.

=============================================

Question 5

Claude is forming a conic section so he could form an ellipse. The other choices (square, pentagon, parallelogram) are not possible cross sections of a cone.