The correct answers are:
Perpendicular cross-section of a pyramid is a triangle.
Perpendicular cross-section of an oblique cylinder is an ellipse.
Parallel cross-section of a sphere is a circle.
When a rectangle is rotated about the y-axis, a cylinder is formed.
When a right triangle is rotated about the y-axis, a cone is formed.
Explanation:
Cutting a cross-section of a pyramid perpendicular to the base would form a triangle. Your "slice" would go from the apex of the pyramid straight to the base. Where the cut goes through the slanted faces of the pyramid would form the slanted sides of the triangle. Where the cut goes through the base of the pyramid would make the base of the triangle.
Cutting a cross-section of an oblique (non-right) cylinder would form an ellipse (oval). Since the cylinder is not right, it is slanted. This means going perpendicular to the base of the cylinder would not go straight (horizontally) through the cylinder; instead it slants, which "stretches" the cross-section, forming an ellipse.
Any cross-section of a sphere is a circle, since a sphere is perfectly round with no base.
When rotating a rectangle about the y-axis, imagine rotating a piece of paper. The shape formed by doing this would "bend" the rectangle around the axis, forming a cylindrical shape.
When rotating a triangle about the y-axis, we can imagine the same situation we did with the rectangle; the difference is that the triangle goes in a point, which means this new figure will be as well. This would make it a cone rather than a cylinder.
