There is a vegetable shed covered with plastic film. It is 50 meters long and its cross section is a semicircle with a radius of 5 cm. How many square meters of plastic film does this vegetable greenhouse use at least?
Cylindrical sink. If a cylindrical glass rod with a radius of 5 cm is put into the water, the water surface will rise by 9 cm. When the glass rod is vertically pulled out of the water by 8 cm, the water surface will drop by 4 cm, and the volume of the glass rod can be calculated.
1. There is a vegetable shed covered with plastic film. It is 50 meters long and its cross section is a semicircle with a radius of 5 cm. How many square meters of plastic film does this vegetable greenhouse use at least?
π× 0.05× 0.05× 2+50× 2× π× 0.05 = 5.05 π (square meter)
2. Cylindrical sink. If a cylindrical glass rod with a radius of 5 cm is put into the water, the water surface will rise by 9 cm. When the glass rod is vertically pulled out of the water by 8 cm, the water surface will drop by 4 cm, and the volume of the glass rod can be calculated.
π×5×5×(8×(9÷4))=450π (cubic centimeter)
Cylindrical application problem
Reward score: 15- settlement time: April 9, 2007 19: 27.
1. The conical grain pile is 2m high and covers an area of10m2. If every cubic meter of millet weighs 500 kilograms, how many kilograms does this pile of millet have?
2. Li Shifu will build a pair of iron chimneys, each with a length of 80cm and a bottom diameter of10cm. How many square meters of iron do you need at least?
The volume of a cylinder is 48 cubic centimeters. How many cubic centimeters is the volume of this cylinder larger than that of a cone with equal base and equal height?
4. A conical tin bucket 15.7 meters high, with a square side area. How much tin does it take to make such a tin oil drum?
5. Cone and cone have the same volume and height. Given that the circumference of the bottom of a cylinder is 18.84 cm, what is the bottom area of the cone?
6. If you cut a 2-meter-long cylindrical wood into two sections, the surface area will increase, for example, 6 square meters. What is the volume of wood?
1) 2* 10*( 1/3)*500
2) [ 10*80+( 10/2)*( 10/2)*3. 14*2]*2
3) 48*( 1/3)
4) 15.7* 15.7+( 15.7/2)*( 15.7/2)*3. 14
5) ( 18.84/3. 14/2)*( 18.84/3. 14/2)*3. 14*( 1/3)
6) 6/2*2
A cylinder with a height of 10 cm will increase its surface area by 125.6 cm if its height is increased by 2 cm. Find the original volume of this cylinder.
When the height increases by 2 cm, the surface area increases by a circle of lateral area, so the radius of the cylinder bottom is125.6 ÷ 2 ÷ 3.14 ÷ 2 =10 (cm). The original volume of the cylinder is 3. 14× 10× 60.
There is a vegetable shed covered with plastic film. It is 50 meters long and its cross section is a semicircle with a radius of 5 cm. How many square meters of plastic film does this vegetable greenhouse use at least?
Cylindrical sink. If a cylindrical glass rod with a radius of 5 cm is put into the water, the water surface will rise by 9 cm. When the glass rod is vertically pulled out of the water by 8 cm, the water surface will drop by 4 cm, and the volume of the glass rod can be calculated.
1. There is a vegetable shed covered with plastic film. It is 50 meters long and its cross section is a semicircle with a radius of 5 cm. How many square meters of plastic film does this vegetable greenhouse use at least?
π× 0.05× 0.05× 2+50× 2× π× 0.05 = 5.05 π (square meter)
2. Cylindrical sink. If a cylindrical glass rod with a radius of 5 cm is put into the water, the water surface will rise by 9 cm. When the glass rod is vertically pulled out of the water by 8 cm, the water surface will drop by 4 cm, and the volume of the glass rod can be calculated.
π×5×5×(8×(9÷4))=450π (cubic
1. The roller of the roller is cylindrical, with a bottom diameter of 1m and a length of 2m. How many roads can you press per roll?
2. A pile of conical yellow sand, with a circumference of 25.12m at the bottom, a height of1.5m, and a weight of1.5t per cubic meter of yellow sand. How many tons does this pile of sand weigh?
3. The freight box is a cuboid with a length of 4m, a width of 1.5m and a height of 4m. It's full of sand. After unloading, the sand accumulates into a cone with a height of1.5m. What is its bottom area?
4. It is known that a cylindrical steel pipe with a length of 30 cm, a long outer diameter and a wall thickness of 65438 0 cm weighs 7.8 grams per cubic centimeter. How much does this steel pipe weigh?
5. A granary full of rice has a conical top and a cylindrical bottom. The circumference of the cylinder bottom is 62.8 meters, the height is 2 meters, and the height of the cone is 1.2 meters ... How many cubic meters of rice can this grain depot hold? If each cubic meter of rice weighs 500 kilograms, how many tons of rice can this grain depot hold? (Keep one decimal place)
6. Cut a cuboid with a square cross section into the largest cone. It is known that the circumference of the cone bottom is 6.28 cm and the height is 5 cm. What is the volume of this cuboid?
7. The cylinder and the cone have the same height, and the volume difference is 50.24 cubic centimeters. If the bottom radius of a cylinder is 2 cm, what is the side area of the cylinder?
Linear ruler
1. On the map with the scale of 1: 7500000, the distance between A and B is 10 cm. When a bus and a truck set off from A and B at the same time, they met for three hours. As we all know, the speed ratio of buses and trucks is 3: 2. How many kilometers does this truck run per hour? How many hours will it take for the bus to get to a place?
Distance between the two places:10 ÷1/7500000 = 7500000 cm = 750 km.
When they meet, the distance of the freight train line is 750÷(3+2)×2=300 kilometers.
Hourly mileage of trucks: 300÷3= 100 km.
Bus speed: 100 ÷ 2× 3 = 150km.
The bus still needs to travel for 750÷ 150-3=2 hours.
2. On the design plan, the teaching building is150m long, 25cm long and15cm wide. What is the scale of the building plane? How many square meters does this building cover?
150m =15000m
25: 15000 = 1:600- ratio
15/ 1:600=9000 (cm) = 90m wide.
150*90= 13500 (m2)-construction area
3. A right triangle steel plate is drawn on the drawing with the scale of 1/200. The two right-angled sides are 5.4 cm long, and the ratio of their lengths is 5: 4. What is the actual area of the steel plate?
5.4 * 5/(4+5)= 3(cm)- Right side of right triangle on the diagram.
5.4-3=2.4 (cm)-the other right side of the right triangle on the drawing.
3/1/200 = 600 (cm) = 6m-the length of the actual right-angle side of the steel plate.
2.4/ 1/200 = 480(cm)= 4.8m- the length of the other right-angled side of the actual steel plate.
6*4.8/2= 14.4 (m2)-actual area of steel plate.
4. Draw a rectangular plot with the length-width ratio of 5: 3 on the map with the scale of 1/500, and the rectangular perimeter is 32 cm. What is the actual area of rectangular land?
32/2 = 16(cm)- the sum of the length and width of the graph.
16 * 5/(3+5) =10 (cm)-the length of the graph.
16- 10=6 (cm)-the width of the graph
10/ 1/500=5000 (cm) = 50m-actual length
6/ 1/500=3000 (cm) = 30m- actual width
50*30= 1500 (square meter)-actual area
5. The distance between Beijing and Shanghai is 1400km. On a map of China, the distance between the two places is 20cm. Find the scale of this map of China.
Thinking: This problem is to find the scale when we know the actual distance and the distance on the map. According to the formula: distance on the map: actual distance = scale, that is, 20 cm: 1400 km. The units in the preceding paragraph and the latter item should be unified. In this problem, it is easier to change 1400 km into cm.
Solution:
20 cm: 1400 km
= 20cm: 140000000cm
= 1:7000000
The scale of this map of China is 1: 7000000.
1. A precision part drawn on paper is 5 mm long and 10 cm long. What's the scale of this painting?
2. The railway line from Lanzhou to Urumqi is about 1900km long, and the distance between the two places is 5cm measured on the map. What's the scale of this map?
The scale of the map is that the distance from Beijing to Tianjin is 4.8 cm. What is the actual distance between the two places?