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
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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.
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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.
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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.
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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.