There is only one height.
2. The volume of the cylinder:
Formula derivation: using the strategy of transformation.
The bottom of the cylinder is divided into 16, 32, 64 ... infinity, and the cut object is getting closer and closer to the cuboid. The volume formula of cylinder is derived from the volume formula of cuboid.
V=sh (bottom area × height)
Of course, there will be some changes in the process of calculating the volume of the cylinder. Such as known radius, diameter, bottom circumference, etc.
For example:
It is known that the bottom radius is 10 cm and the height is 12 cm. Find the volume of a cylinder.
Given that the diameter of the bottom surface is 4 decimeters and the height is 8 decimeters, find the volume of the cylinder.
It is known that the circumference at the bottom of the cylinder is 12.56 decimeters and the height is 5 decimeters. Find the volume of a cylinder.
3. The volume of the cone:
Through observation and discussion, it is concluded that the volume of a cone is 1/3 () of the volume of a cylinder with equal bottom and equal height, and the volume of a cylinder is three times that of a cone with equal bottom and equal height.
V= 1/3sh
4. In the next research, we will encounter some extensions and improvements of the cone.
(1) The volume ratio of a cylinder with equal base and equal height to a cone is 3: 1.
For example, the volume of a cylinder is 24 cubic meters, and the volume of a cone with equal bottom and equal height is ().
(2) The ratio of the bottom area of a cylinder with equal volume and equal height to the bottom area of a cone is1:3;
Cylinders and cones are equal in volume and height. It is known that the bottom area of a cone is 6 square centimeters and that of a cylinder is ().
(3) The ratio of the height of a cylinder with equal volume and equal bottom area to the height of a cone is 1: 3.
Cylinders and cones have the same area and volume. It is known that the height of the cylinder is 15cm and the height of the cone is () cm.
5. Practice on the volume of cone
(1) The base area of the cone is 170 cm2 and the height is 12 cm. What is the volume of this cone in cubic centimeters?
(2) Cast an iron block with a volume of 282.6 cubic centimeters into a conical machine part with a bottom radius of 6 centimeters, and find the height of the conical part.
(3) Immerse the conical iron block into a container with a bottom radius of 6 cm and a water depth of 20 cm, and the water surface rises to 22 cm. What is the volume of this conical iron block?
(4) Conical sand pile with bottom area of12.56m2 and height of 6m. How many meters can a road with a thickness of 2 cm be paved on a road with a width of 10 meter?
(5) Casting a cylindrical steel block with a bottom radius and a height of 8 decimeters into a cone with the same height. How many square decimetres is the bottom area of this cone?