Solution:

Shapes that can stand up by themselves are 3D shapes. A cylinder has 2 identical circle shaped faces on the top and bottom and its width is the same all the way from top to bottom. A cone and a pyramid both have a pointed top. Which objects in the picture can stand up by themselves and have a pointed top? In the first row, the popcorn cone is a cone and the pyraminx puzzle is a pyramid. In the second row, the blue object is a pyramid.

Solution:

1. Cut the cone horizontally in the middle and the new face we get is called a cross section. The cross section of a cone is a circle. The closer to the bottom, the larger the circle gets. So, ② is the correct answer. ① is incorrect because the two circles are the same.
2. The cross section of a pyramid is the same shape as its bottom face, but smaller in size. In the picture, the bottom face is a square. So, the cross section should also be a square. ② is the correct answer.

Solution:

The 1st shape is a cone. After we unfold it, we'll get a smaller circle and a section of a larger circle. So, link the cone to ②. The 2nd shape is a triangular pyramid. Its faces on the bottom and on the sides are all triangles. So, link the triangular pyramid to ①. The 3rd shape is a pentagonal pyramid. Its bottom face is a pentagon, with 5 sides. Its faces on the side are all triangles. So, link the pentagonal pyramid to ③.