I have a lot of math review questions for the sixth grade of primary school!
5. Calculation of perimeter and area.
1, find the area of the shaded part in the figure. (Unit: cm)
2. Uncle Zhang surrounded a trapezoidal vegetable field with one side against the wall (as shown below). The fence is 48 meters long. If you collect 9.5 kilograms of cabbage per square meter, how many kilograms of cabbage can you collect in this land?
3. The school has a rectangular open space, which is 50 meters long and 20 meters wide. The area left by this open space should be afforested. Plant flowers in the area where the green space is used, and plan the largest triangle lawn in the remaining area. Please design it and draw a sketch. (scale 1: 1000)
4. There is a triangular green space with an area of180m2 in the park (as shown below), with a base length of 24m. Green space expansion, the bottom extends 8 meters, and the height remains unchanged.
(1) Please draw an expanded triangular green space on the picture below. (just drawing a schematic diagram)
(2) Calculate the total area of the expanded triangular green space with the formula.
5. Ring flower beds should be built in front of activity rooms in residential areas. It is known that the perimeter of the flower bed is 37.68 meters.
(1) The area of this circular flower bed is () square meters.
(2) Please draw the plane of this circular flower bed on the scale of 1: 400 (indicate the center and radius), and the radius of the flower bed in the figure is () cm.
Calculation of surface area and volume of intransitive verbs.
1, find the volume of hollow machine parts. (Unit: cm)
2. In a rectangular box with length, width and height of 2 decimeters, 2 decimeters and 5 decimeters respectively, just a cylindrical object can be put down (as shown below). What is the maximum volume of this cylindrical object? How many cubic decimeters is the free space in the box?
3. The school will donate a batch of teaching materials to Hope Primary School, including 24 boxes of chalk, each box is packed with a cube with a length of 1 decimeter.
(1) Please design a rectangular box to hold the chalk.
The internal dimensions of the packaging box you designed are: length (), width () and height ().
(2) How much paper does the packing box you designed need? (Ignored at joints)
Liquid drinks are sealed and packed in a rectangular plastic paper box. Measured from the outside, the box is 6 cm long, 4 cm wide and 10 cm high. The box surface is marked with "net content: 240ml". Please analyze whether the description is false.
Before the arrival of the summer heat in 2006, a well-intentioned person was prepared to donate money to build a standardized swimming pool, 60 meters long and 60 meters wide.
(1) What is the area of this swimming pool?
(2) How many cubic meters have you dug for this swimming pool?
(3) spread a layer of cement on the edge and bottom of the pool. What is the area of cement?
6. To make a cylindrical bucket without a lid, there are the following kinds of iron sheets to choose from. (Unit: decimeter)
(1) The material you selected is ().
(2) What is the volume of the bucket made of the material you choose?
7. A children's toy-gyro (as shown below), with a cylinder above and a cone below. After testing, only when the cylinder diameter is 3 cm, the height is 4 cm, and the height of the cone is the height of the cylinder, can it rotate stably and quickly. What is the volume of this gyro? (Keep the whole cubic centimeter)
Seven, ability training.
1, the lower bottom of the isosceles trapezoid is twice as large as the upper bottom. Divide it into four trapezoids with the same area and shape. Please try it.
The picture below shows a square with a side length of 6 cm. E and f are the midpoint of CD and BC respectively. Find the area of the shaded part.
3. The following figure shows two identical equilateral triangles with a point A..
(1) Draw three vertical lines from point A to three sides of the triangle and measure the total length of the three vertical lines.
(2) Choose another point B in the triangle, make three vertical lines on three sides of the triangle, and measure the total length of the three vertical lines. See what you can find and write down your findings.
4. Find the volume of glue skillfully.
A glue bottle (as shown below) has a cylindrical body (excluding the bottleneck) and a volume of 32.4 cubic centimeters. When the bottle is inverted, the height of the glue in the bottle is 8 cm, and when the bottle is inverted, the height of the excess part is 2 cm. Please calculate how many cubic centimeters of glue are there in the bottle?