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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?
Let the volume of the second cylinder be x cubic centimeter, 4:5 = 3.2: X, & nbsp; 4x = 3.2 × 5, & nbsp; 4x = 16, & nbsp; & nbsp; X = 4; 4-3.2 = 0.8 (cubic centimeter); answer: the volume of the second cylinder is 0.8 cubic centimeter more than that of the first one
A part with a bottom diameter of 5 cm and a height of 10 cm is cut down along one of its bottom diameters and cut into two parts of the same size. How many square centimeters is the total area increased from the original? (2) What is the surface area of each half part? What's the volume?
(1) 10 × 5 × 2 = 100 (square centimeter); answer: the total area is increased by 100 square centimeter; (2) [3.14 × (5 △ 2) 2 × 2 + 3.14 × 5 × 10] △ 2 + 10 × 5, = 98.125 + 50, = 148.125 (square centimeter); 3.14 × (5 △ 2) 2 × 10 △ 2, = 196.25 △ 2, = 98.125 (cubic centimeter); answer: the surface area of each half part is 148.125 square centimeter, and the volume is 98.125 cubic centimeter
The sum of the volumes of a cylinder and a cone is 130 cubic centimeters. The height of a cone is twice that of a cylinder. The area of the bottom of a cone is 23 times that of a cylinder. How many cubic centimeters are the volumes of a cylinder and a cone?
Let the height of the cylinder be h, then the height of the cone be 2h, the area of the bottom of the cylinder be 3S, then the area of the bottom of the cone be 2S, so the volume of the cylinder is 3SH, and the volume of the cone is: 13 × 2S × 2H = 43sh, because: 3SH + 43sh = 130, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 9sh + 4sh = 390, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 13SH = 390, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &So the volume of cylinder is 3 × 30 = 90 (cubic centimeter) and that of cone is 43 × 30 = 40 (cubic centimeter). A: the volume of cylinder is 90 cubic centimeter and that of cone is 40 cubic centimeter
RELATED INFORMATIONS
- 1. 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?
- 2. Super difficult exercises of solving cylinder and cone More is better! Thank you very much!
- 3. How to do the problem of cutting off the remaining volume of a small cone in a cone The poem goes like this: on a cone with a bottom radius of 6 decimeters, cut off a cone with a bottom radius of 3 decimeters. The known cut off part is the volume of 27 cubic decimeters
- 4. A drawer principle problem, but also analysis The summer camp organizes activities for 200 students, including visiting famous schools, surfing on the sea and mountain climbing. It is stipulated that each student must participate in one or two activities, so how many students participate in the same activities at least?
- 5. A question about the principle of drawer There are five arbitrary points in the rectangle with 6cm and 8cm sides (including the boundary). The distance between at least two of the five points is less than 5cm. Why?
- 6. 1. From 1 to 36, how many numbers can be taken at most so that the difference between the two numbers is a multiple of 5? 2.1 to 100, take at least several numbers to ensure that one of them must be divisible by 5?
- 7. The topic of drawer principle 1. Proof: in any five integers, three numbers must be taken out, so that their sum can be divided by three 2. A school sent 204 students to plant 15301 trees on the mountain, among which at least one person planted 50 trees and at most one person planted 100 trees, proving that trees planted by at least five people were the same
- 8. On the principle of drawer Among the six monkeys on monkey mountain, one must have got at least five peaches. How many peaches are there in this pile?
- 9. If x and y are inversely proportional and y = 12 when x = 16, then when x = 10, y = ()
- 10. This is our teacher Li
- 11. 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
- 12. There are 32 bottles of 100kg oil. How many large and small oil bottles are there?
- 13. There are 50 chickens and 160 feet in the same cage. If all chickens are assumed to be rabbits, then 50 rabbits will have (?) feet, which will be more than the actual (?): Why are there so many more chickens? Because if a chicken is assumed to be a rabbit, it will have (?) feet, which will be more than the actual (?) = (?), we need to divide (?) by (?) = (?) if a chicken is assumed to be a rabbit, then rabbits will have (?) - (?) = (?)
- 14. Put 7 pieces of iron into 3 boxes, at least 3 pieces of iron sheet should be put into the same box. Why?
- 15. A+A+A+A+A=100 (B + b) / (division sign) a = 100 B+A+B+A-C=100 Then: a = () B = () C = ()
- 16. 1. A barrel of oil weighs 40 kg. After four fifths of the oil is poured out, the barrel weighs 12 kg. How many kg of oil is there in the barrel? 2. The number of school art group is six more than that of sports group, and the number of sports group is one fifth less than that of art group. The number of calligraphy group is four fifths of that of art group. How many people are there in calligraphy group?
- 17. A math problem, urgent, fast! Sixth grade, to process! There are several machine parts. Every 12 parts are packed in a box, there are 11 more. Every 18 parts are packed in a box, there is one less. Every 15 parts are packed in a box, and there are seven more than two. It is known that the parts are between 300 and 400. How many parts are there? Thank you
- 18. The sum of a and B is 1.98. If the number of a is reduced to one tenth of the original number, then the ratio of a and B is 1:1. What is the original number of a and B?
- 19. Sixth grade mathematics problems, to process When a runs three eighths of the whole race, B runs one third of the race. After that, a's speed will not change, B's speed will increase. When both of them reach the finish line at the same time, B's speed will increase by ()% It takes 12 hours (including 12 hours) at most for a ship to carry fuel. When it leaves, it travels 30 kilometers per hour. When it returns along the original road, its speed is 8% of that when it goes. How many kilometers can the ship return?
- 20. 1. Try to prove that: if 19 points are placed in a square with one side length, and any three points are not on a line, then there is at least one triangle with these points as its vertex, and its area is not more than 1 / 18 2. Any five integers, will be able to choose three integers, so that their sum is divided by 3