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Super difficult exercises of solving cylinder and cone More is better! Thank you very much!
The volume of a cone is 45 cubic centimeters. If its bottom radius is reduced to one third of the original and its height is expanded to two times of the original, what is its volume?
The volume of a cylinder and a cone is equal. The ratio of the height of the cylinder to the height of the cone is 4:9. The bottom area of the cone is 20 square centimeters. How many square centimeters is the bottom area of the cylinder?
There is water in the cylindrical glass. The water surface is 5cm high and the bottom diameter is 8cm. After the cylinder with the bottom diameter of 4cm and height of 6cm is vertically placed in the glass, the water surface does not submerge the cylinder. How many cm is the water surface high?
There are two cylindrical containers a and B. at first, container a contains 2 liters of water, and container B is empty. Now, water is injected into the two containers at a flow rate of 0.4 liters per minute. After 4 minutes, the water surface heights of the two containers are equal. Suppose the bottom radius of B is 5 cm, then what is the bottom diameter of a?
A cylinder with a radius of 4cm at the bottom and a height of 9cm is cut into the largest cone. What is the volume of the cone in cubic centimeter? What is the volume of the cut part? (π = 3)
The volume of the cylinder is: 3 × 42 × 9, = 3 × 16 × 9, = 432 (cubic centimeter); the volume of the cone is: 432 × 13 = 144 (cubic centimeter); the volume of the cut part is 432 × 23 = 288 (cubic centimeter); a: the volume of the cone is 144 cubic centimeter, and the volume of the cut part is 288 cubic centimeter
Proof of volume ratio of cone in Senior High School
Proof: the ratio of the volume of the small cone to the volume of the original cone obtained by cutting the cone parallel to the bottom plane of the cone is equal to the cube of the ratio of the height of the small cone to the height of the original cone
Because they are parallel sections, the proportions of radius and height are equal. Just list the expressions of two volumes and compare them
The calculation will come out soon
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- 11. Exercises of cylinder and cone 1. The bottom surface of a cylinder is divided into several sectors, and then cut into an approximate cuboid. The surface area of the cuboid is increased by 200 square centimeters. Given that the height of the cylinder is 20 cm, the volume of the cylinder is calculated 2. In a cylindrical glass container with a bottom radius of 10 cm and a water depth of 8 cm, a piece of iron with a length of 8 cm and a width of 15 cm and a height of 10 cm should be put into the container ① If you put the iron in the water, how many centimeters will the water rise? ② If you put the iron in the water, how many centimeters will the water rise?
- 12. There are two equal bottomed cylinders. The height of the first cylinder is 45 times that of the second cylinder. The volume of the first cylinder is 3.2 cubic centimeters. How many cubic centimeters more is the second cylinder than the first one?
- 13. Fill in the blanks: 1. The radius ratio of a cylinder to a cone is 2:3, the height ratio is 3:2, and the volume ratio is（ 2. If the bottom radius of the cone is constant and the height is increased by 2 times, the volume is () times of the original. If the height of the cone is constant and the bottom radius is increased by 2 times, the volume is () times of the original 3. There is a piece of iron sheet, which can be used for 8 sides of cylindrical oil drums or 24 bottoms of cylindrical oil drums of uniform specifications. Ten pieces of iron sheet can be used for () such oil drums No need to write process
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- 17. A+A+A+A+A=100 (B + b) / (division sign) a = 100 B+A+B+A-C=100 Then: a = () B = () C = ()
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