一、填空题：15分
1、The top and bottom of a cylinder are two ( ) circles with ( ) faces that are curved; the base of a cone is a ( ) shape and the side is a ( ) face.
2. The area of the ( ) of the cylinder plus the area of the ( ) is the surface area of the cylinder.
3, scale = ( ): ( ), scale is actually a ( ).
4, a map of the scale is . A, B two places are 140km away from each other, drawn on this map should be ( ) cm.
5, with a length of 31.4 centimeters, the width of 20 centimeters of the rectangle of a piece of paper into a cylinder, the length of this piece of paper is the cylinder of the ( ), the width of the cylinder of the ( ).
6. The side of a cylinder is unfolded as a square with a side length of 8 cm. The side area of this cylinder is ( ) cm2.
7. A part is 8 millimeters long and is 16 centimeters long when drawn on a design drawing, which has a scale of ( ).
8, sixth-grade students lined up to do radio exercises, the number of people in each row and the number of rows formed into ( ) proportional; a certain rate of oil, the mass of peanut oil and the mass of peanuts, into ( ) proportionality; 3x = y, x and y into ( ) proportionality; the actual distance is a certain, the distance on the map and the scale into ( ) proportionality.
9, the ratio of the radii of the bases of two cylinders of equal height is 4:3, and the ratio of their volumes is ( ).
10, 4.6 m 2 = ( ) decimeters 2 5600 decimeters 3 = ( ) meters 3
7.08 liters = ( ) liters ( ) milliliters 3dm350cm3 = ( ) dm3
11, a conical part, the radius of the base is 6dm, the height of the radius of the radius of the half of this part of the volume of the ( ） dm3.
12, to a A cylinder is divided into equal parts and cut to form an approximate rectangle. The base area of this rectangle is 7 square decimeters, the height is 8 decimeters, and the volume of the cylinder is ( ) cubic decimeters.
14, a cylindrical pool of cement to be smeared on the inner walls and bottom, the diameter of the bottom of the pool is 4 meters, the pool is 15 decimeters deep. The area to be cemented is ( ) square meters.
15, the front wheel of the road roller is cylindrical, wheel width 4m, diameter 1.5m, the front wheel rotates a week, the area of the road is ( ) m2.
16, in a plan, 5 cm line segment represents the actual distance of 50 meters. The scale of this map is ( ).
17. A cone has a volume of 4.5 cubic decimeters, a height of 4.5 decimeters, and a base area of ( ) square decimeters.
18, The volume of a cone with a base area of 30 square centimeters and a height of 5 centimeters is ( ) cubic centimeters, and the volume of a cylinder with the same base and height as it is ( ) cubic centimeters.
19, the volume of 56.52dm3 of iron fused into a base diameter of 12 dm cone parts, the height of the cone is
( ) dm.
Two, judgment questions: 10 points
1, the area of a parallelogram is certain, its base is inversely proportional to the height. ( )
2. For a wire, the number of meters used is inversely proportional to the number of meters left. ( )
3. The number of copies of a subscription to Junior Literature is inversely proportional to the total amount of money. ( )
4. The base area of a rectangle is certain and the height and volume are inversely proportional. ( )
5. The radius and area of a circle are directly proportional. ( )
6. The base of a cylinder has a diameter of 3 centimeters, a height of 3π centimeters, and the sides unfold as a square. ( )
7. When the height of a cylinder is enlarged by a factor of two, the volume is enlarged by a factor of two. ( )
8. The volume of a cone is equal to 13 of the volume of a cylinder. ( )
9, The volume of a rectangle, square and cylinder with equal base and height is equal. ( )
10, An object whose upper and lower faces are equal circles is probably a cylindrical object. ( )
Three, multiple-choice questions: 10 points
1, a square block of wood with a prism length of 4 decimeters cut into a maximum cylinder, the volume is ( ) cubic decimeters.
A, 50.24 B, 100.48 C, 64
2. A cylinder has ( ) heights and a cone has ( ) heights.
A, 1 B, 2 C, countless
3, The radius of the base of a cylinder is r and the height is h. Its surface area is expressed as ( )
A, 2πrh B, 2πr? + 2πrh C, πr? + 2πrh
4, A cylinder, the diameter of the base and the height of the base are 2 decimeters, and the surface area of this cylinder is ( ) square decimeters.
A、6π B、5π C、4π
5、The radius of the base and the height of a cylinder are enlarged by a factor of 2, and its volume is enlarged by a factor of ( ）
A、2times B、4times C、8times
6、The length of a machine part is 8 millimeters, and the length of it drawn on a drawing with a scale of 10:1 is ( ）
A、8 decimeters B, 8 millimeters C, 8 centimeters
7, The circumference and diameter of a circle ( ).
A, proportional B, inversely proportional C, not proportional
8, the length of a rectangle is certain, its perimeter and width ( ).
A. positively proportional B. inversely proportional C. disproportional
9. The two quantities in ( ) are not proportional.
A, the average speed and time taken by a train traveling from Beijing to Guangzhou
B, a box of apples, the number of pieces eaten and the number of pieces left.
C, the height of an object and the length of its shadow at the same time and place.
10, Xiao Ming's height and weight ( )
A, proportional B, inversely proportional C, disproportionate
4, Calculation:
1, Calculate the surface area of the following three-dimensional figure: 4 points
2, Calculate the volume of the following three-dimensional figure: 8 points
3, Recurring equation: 12 points
( 7.5 + 2.5) × 0.25 710-18 × 4 5.4 ÷ 18 + 12
2 ÷ 85 × 2524 2.25 × 1.8 + 12.5 × 0.18 [1 - (12 + 13 )] × 36
V. Graphics and Operations (11 points)
1, There is a rectangular piece as shown on the right: measure its length and width.
Then find the actual lengths of its length and width on a scale of 15000.
And find how many square meters is its actual area? (Take the number of whole centimeters)
(1+2+2 points)
2. The relationship between the number of notebooks bought and the amount of money is shown in the following table:
Quantity/book 0 1 2 3 4 5 6 7 ...
Total amount of money/$0 1.5 3 ...
(1) Complete the table and find the actual length of the notebook according to the data in the table, trace the points in the graph and then connect them in order. (1+1 points)
(2) Which quantity did not change? (1+1 point)
(3) From the diagram, how much money is needed to buy 9 notebooks?1 point
3. The movie theater is 60° north east of the center square, and the actual distance according to the center square
is about 240 meters away from the place. Mark the location of the movie
theater on the diagram. (2 points)
VI. Problem solving: 24 points
1, a kind of beverage cans in the shape of a cylindrical bottom diameter of 6 centimeters, the height of 10 centimeters, according to the above figure into a cardboard box, the volume of this box is at least how many cubic centimeters?
2. Can the glass shown on the left hold 400 milliliters of Huiyuan juice?
3, a pile of conical sand, the bottom circumference is 6.28 m, the height of 1.2 m, each cubic meter of sand weighs 1.5 tons. How many tons does the pile of sand weigh?
4. A glass jar with a base area of 1.5 square decimeters contains a stone as shown in the figure. The depth of the water is 18 centimeters, and the water drops to 15 centimeters after the stone is taken out. what is the volume of the stone?
5. What is the minimum area of tin to be used to make 20 sections of cylindrical tin ventilation pipe with a base radius of 5 cm and a length of 40 cm?
6. On a map with a scale of 1:5,000,000, the distance from city A to city B is measured to be 9 centimeters. A car traveling from city A to city B at 80 km per hour will reach city B in 5 hours?
VII, additional questions:
1, two cylinders of 2 meters long with equal base area into a cylinder steel, the surface area is reduced by 0.6 square decimeters, if each cubic decimeter of steel weighs 7.8 kilograms, how many kilograms of this steel after the assembly?
2, a cylinder cut and put together into an approximate rectangle, the surface area increased by 6 square centimeters, the height of the rectangle is known to be 3 cm, find the volume of the cylinder.