1, the ratio of the radius of the cylinder bottom to the radius of the cone bottom is 3: 4, that is, the radius of the cylinder bottom is three quarters of the radius of the cone bottom, the volume of the cylinder is sh, and the volume of the cone is one third Sh. If the bottom radius of the cylinder is 3r, the height of the cylinder is h, the height of the cone is h, the bottom radius of the cone is 4r, and the ratio of the height of the cone to the cylinder is 27: equal based on volume.
2. Side area of the cylinder: expand the side of the cylinder along the height direction to get a rectangle (square). The length of the rectangle is the circumference of the bottom of the cylinder, and the width of the rectangle is the height of Yuanzu, so lateral area = bottom circumference × height = π× diameter × height =2×π× radius × height. Area of cylinder side =ch=πdh=2πrh.
3. Volume of the cylinder: firstly, the cylinder is cut into two halves along the diameter, and then cut into several parts along the radius, which are embedded together to form an approximate cuboid. The bottom area of this cuboid is equal to the bottom area of the cylinder, and the height is equal, so the volume is equal.
The length of an approximate cuboid is half the circumference of the cylinder bottom (πr), and the width is the radius of the cylinder bottom (r), which is higher than the height of the cylinder (h), so the volume of the cylinder = the area of the bottom × the height =πrh.
4. The volume of cone: it is the result of experiments with cylinders and cones with equal bottoms and heights. Fill the cone with water, then pour it into a cylinder with equal bottom and equal height, and fill it exactly three times. Therefore, on the premise of equal bottom and equal height, the volume of a cone is the volume of a cylinder or the volume of a cylinder is three times that of a cone. The volume of the cone =sh=πrh.
The importance of learn mathematics:
1. Mathematics is closely related to our life. To say that the real effect of learning mathematics is not reflected in exam-oriented education, but in my own thinking about the future.
2. The importance of mathematics is self-evident. Mathematics is the foundation of all sciences and an important channel to cultivate logical thinking. It can be said that every major progress of our mankind is strongly supported by mathematics.
3. The application of mathematical knowledge in life is everywhere. From the calculation of daily living costs, to astronomy, geography, quality control, agricultural economy, aerospace, there are shadows of using mathematics.