Window of knowledge (1.5 points per grid, ***27 points)
1, along the high shear of the cylinder, one side is equal to () of the cylinder, and the other side is equal to () of the cylinder.
2, cuboid, cube, cylinder volume calculation formula can be written as ().
3, 3.6 cubic meters = () cubic decimeter
8050ml = () L。
4. Put the square paper with a side length of 6 decimeters into the cylindrical paper tube (excluding the joint). The side area of this paper tube is () square decimeter and the volume is () cubic decimeter.
5. The conical container filled with water is 9 cm high. If all the water is poured into a cylindrical container with the same bottom and height, the height of the water is () cm.
6. There is a cylindrical tank with a height of 1 decimeter and a bottom circumference of 6.28 decimeter. The maximum area of the trademark paper on the side of the box is () square decimeter. To make this box, you must use at least () square decimeter of iron, and its volume is () cubic decimeter.
7. The volume of the cone is 15 cubic meters, the height is 6 meters, and the bottom area is () square meters.
8. Cut a cube with a length of 2 decimeters into the largest cylinder, and the volume of this cylinder is () cubic decimeters.
9. The area and volume of the bottom of the cylinder and the cone are equal respectively. Suppose the height of the cylinder is 6 cm and the height of the cone is () cm.
10, and the volume difference between a cylinder with equal bottom and equal height and a cone is 16 cubic meter. The volume of this cylinder is () cubic meters, and the volume of this cone is () cubic meters.
Please be the referee (2 points for each question, *** 10).
1, the volume of cylinder is greater than the volume of cone ()
2. The volume of the cone is equal to 1/3 () of the volume of the cylinder.
The volumes of two cylinders are equal, so their surface areas are equal. ()
When the height of a cylinder is doubled, its volume is also doubled. () 5. The diameter of the bottom of the cylinder is 3 cm and the height is 9.42 cm. When the side is unfolded, it is a square. ( )
Three. Happy ABC (2 points for each question, *** 10)
1, how many liters of water are filled in the cylindrical barrel, that is, find the barrel ().
A, lateral area B, surface area C, volume D, volume
2. Compare the volumes of cylinders, cubes and cuboids with equal bottoms and heights. ()
A, the cube is big b, the cuboid is big c, and the cylinder is big d, with the same volume.
3. When the side surface of the cylinder is square, the height of the cylinder is higher than its bottom surface ().
A. radius B. diameter C. perimeter D. area
4. How much road surface can be pressed by a roller in one week is the roller ().
A, surface area b, side area c, volume
5. Cut the cube with a side length of 4 decimeters into the largest cylinder with a volume of () cubic decimeters.
a、50.24 B、 100.48 C、64
Four, life through train (***53 points,)
1. Pour 120 liters of gasoline into a cylindrical oil drum with a bottom area of 25 square decimeters. How high is the oil level?
2. The bottom radius of the cylindrical gasoline tank is 2 decimeters and the height is 5 decimeters. How many square decimetres of iron sheet does it take to make this tank? How many liters is its volume?
3. Build a cylindrical pool. The bottom surface is 4m in diameter and 1.8m in depth. What is the minimum area to draw its bottom and sides?
There are four columns in the school auditorium. The circumference of the bottom of each column is 25. 1.2 decimeter, and the height is 5 meters. If 0.5 yuan is per square meter, how much does it cost to paint these four pillars?
5. Conical sand pile with a bottom area of18m2 and a height of1.5m.. If each cubic meter of sand weighs 1.6 tons, how many tons does this pile of sand weigh?
6. There is a cone-shaped sand pile with a bottom area of 3.6 square meters and a height of 2 meters. How thick can you spread the sand in a rectangular bunker 4 meters long and 2 meters wide?
7. Saving water is the duty of every pupil. The diameter of tap water pipe used in schools is 0.2 decimeter, and the flow rate of tap water is generally 5 decimeters per second. How many liters of water will you waste if you forget to turn off the tap?
It's amazing that you can do additional questions (each question 10 points, ***20 points).
1. In a cylindrical container with a diameter of 20 cm, put a conical iron block with a bottom radius of 3 meters and completely immerse it in water. At this time, the water level rose by 0.3 cm. What is the height of the tapered iron block?
2. After cutting the 4-meter-long cylindrical steel into two equal parts, the surface area increased by 0.28 square decimeter. If steel weighs 7.8 kilograms per cubic decimeter, how many kilograms does this steel weigh?
Reference answer
One,
1, perimeter of rectangular height and bottom
2. Bottom area × height
3、3600 8.05
4、36 36
5、3
6、6.28 12.56 3. 14
7、7.5
8、6.28
9、 18
10、24 8
Second,
1、×
2、×
3、×
4、√
5、√
Third,
1、D
2、D
3、C
4、B
5、C
Fourth,
1, 120÷25=8 (decimeter)
Answer: The oil level is 8 cm high.
2. l = 2× 2× 3.14 =12.56 (decimeter) s side = 12.56×5=62.8 (square decimeter) s bottom = 2× 2× 3.1.
Answer: This barrel must use at least 87.92 square decimeters of iron, with a volume of 62.8 cubic decimeters.
3.S side = 4× 3.14×1.8 = 22.608 (square meter) S bottom =4×3. 14= 12.56 (square meter).
S=S side +S bottom = 22.608+12.56 = 35.168 (square meter)
Answer: at least 35. 168 square meters should be painted.
4.25. 12 square decimeter =0.25 12 square meter s side =0.25 12×5= 1.256 (square meter)
1.256× 0.5× 4 = 2.512 (yuan)
A: It costs 2.5 12 yuan.
5. V =1/3×18×1.5 = 9 (cubic meters) 9× 1.6= 14.4 (tons).
Answer: Weight 14.4 tons.
6.V=3.6×2=7.2 (m3) S =4×2=8 (m2) H=7.2÷8=0.9 m.
A: It's 0.9 meters high.
7.0.1× 0./kloc-0 /× 3.14 = 0.0314 (square decimeter) V=0.03 14×5=0. 157.
0. 157×60=9.52 (square decimeter) =9.42 (liter)
A: 9.42 liters of water are wasted every minute.
Six,
1, v =10×10× 3.14× 0.3 = 94.2 (cubic centimeter) s bottom = 3× 3.14 = 28.26 (square centimeter)
H = v \s bottom×3 = 10 (cm)
Answer: cone height 10 cm.
2, 4 meters =40 decimeter V=0.28÷2×40=5.6 (cubic decimeter) 5.6×7.8=43.68 (kg)
This kind of steel weighs 43.68 kilograms.
I wish you progress in your studies and happiness in your life!
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