Analysis: This question does not require area. It is only required that the length and width are several times the diameter of the circle, and then the product of the multiples of the length and width is found.
1 m 20cm =120cm
120÷30=4 90÷30=3
4×3= 12 (block)
A: You can cut 12 pieces at most.
2. A cylinder with a bottom radius of 1 decimeter has a square profile. What is the surface area and volume of this cylinder?
Analysis: Starting from the square of the side expansion diagram, we can know that the height of this cylinder is the circumference of the bottom of the cylinder.
Surface area of cylinder:
(3. 14× 1×2)×(3. 14× 1×2)+3. 14× 1× 1×2
=6.28×6.28+6.28
=6.28×7.28
=45.7 184 (square decimeter)
Cylinder volume:
3. 14× 1× 1×(3. 14× 1×2)
=3. 14×6.28
= 19.7438+092 (square decimeter)
A: The surface area of this cylinder is 45.75438+084 square decimeter, and the volume is 19.38+092 square decimeter.
A train departs from Station A at 8 am and arrives in bilibili at 9 pm the next day. As we all know, the average speed of trains is 98 kilometers per hour. How long is the railway between Station A and bilibili?
Analysis: The key to solve this problem is to know the running time of the train.
24-8+9=25 (hours) [or: 12-8+ 12+9=25 (hours)]
98×25=( 100-2)×25
=2500-50
=2450 km
A: The railway between Station A and bilibili is 2450 kilometers long.
4. The radii of circle and sector are equal. It is known that the area of a circle is 30 square centimeters and the central angle of a sector is 72 degrees. Find the area of the sector.
Analysis: Because the radii of a circle and a sector are equal, the area of a circle and a sector should be multiple. This multiple is the multiple relationship between their central angles.
72 ÷ 360 = 1/5, 30× 1/5 = 6 (square centimeter)
The area of this sector is 6 square centimeters.
Question 1 1: Draw a sector in a circle with a radius of 3 cm so that its area accounts for 20% of the area of the circle, and calculate the area of this sector.
Analysis: This question is the same as the previous one.
3. 14×3×3×20%=5.652 (square centimeter)
A: The area of this area is 5.652 square centimeters.
5. The school assigned the task of planting trees to the sixth and fifth grades in the ratio of 5: 3. The actual tree planting in the sixth grade was 108, exceeding the original task by 20%. How many trees were planned to be planted in the fifth grade?
Analysis: The number of trees originally planned for the sixth grade is the key to solving the problem.
/kloc-How many trees were originally planned to be planted at Grade 0 and Grade 6?
108 ÷ (1+20%) =108× 5/6 = 90 (tree)
2. How many trees were planned to be planted in the fifth grade?
90÷5×3=54 (tree)
Comprehensive formula:
108÷( 1+20%)÷5×3
=90÷5×3
=54 (tree)
A: It was originally planned to plant 54 trees in the fifth grade.
6. Two engineering teams, Party A and Party B, completed a section of road, and the working efficiency of Team A was 3/5 of that of Team B. The two teams completed two-thirds of the road in six days, and the rest was repaired by Team B alone. How many days will it take to finish it?
Analysis: Finding the working efficiency of two teams is the key to solving the problem.
1. What is the sum of the work efficiency of the two teams?
2/3÷6= 1/9
2. How efficient is Team B?
1/9×[5÷(3+5)]
= 1/9×5/8
=5/72
3. How many days will it take to complete?
( 1-2/3)÷5/72
= 1/3×72/5
=24/5 (days)
A: It will take another 24/5 days to complete.
7. A cement factory produced 232,400 tons of cement last year, and the output in the first five months of this year is equal to that in the whole year of last year. According to this calculation, the output of this cement plant will increase by a few percent this year compared with last year.
Scheme 1: The analysis shows that the output will increase in the last seven months of this year, so we have to calculate the output in the last seven months first.
232400÷5×( 12-5)
=46480×7
=325360 (ton)
325360÷232400= 1、4= 140%
Scheme 2: "1" with the unit of 232,400 tons,
1. Compared with last year, what is the average monthly output this year?
1÷5= 1/5
2. How much has the output increased this year compared with last year?
1/5×( 12-5)=7/5
Compared with last year, what percentage has the output increased this year?
7/5= 1.4= 140%
Comprehensive formula:1÷ 5× (12-5) =1.4 =140%.
Answer: This factory increased production this year 140% compared with last year.
8. The kindergarten bought 40 towels of different sizes, which cost 258.8 yuan. The unit price of a large towel is 0. 1 1 yuan, which is twice that of a small towel. What is the unit price of these two towels?
If the unit price of a small towel is X yuan, then the unit price of a large towel is (2x+0. 1 1) yuan.
[x+(2x+0. 1 1)]×40 = 258.8
3x=6.47-0. 1 1
x = 6.36 \3
x=2. 12
2x+0. 1 1 = 2. 12×2+0. 1 1
=4.35
A: The unit price of large towels is 4.35 yuan each, and the unit price of small towels is 2. 12 yuan each.
9. A room with a length of 4-8m and a width of 3-6m needs 768 square bricks with a side length of 0,15m. How many tiles does a room 6 meters long and 4-8 meters wide need? How many square bricks with a side length of 0 or 2 meters should be used in the first room? (Use proportional solution)
Analysis: The area of the room is fixed, and the area of each brick is inversely proportional to the number of blocks.
Suppose it needs x blocks.
0. 15×0. 15x =6×4.8
x =6×4.8÷0. 15÷0. 15
x = 1280
A: Yes 1280 yuan.
Suppose y is needed.
0.2×0.2y=4.8×3.6
y=4.8×3.6÷0.2÷0.2
y=432
A: It's 432 yuan.
10. Shipborne diesel can be used for up to 6 hours. When it leaves with the wind, its speed is 30 kilometers per hour. When it returns with the wind, the distance it travels every hour is 4/5 of that when it leaves with the wind. How far should the ship go backwards at most?
Analysis: The distance traveled by a ship is constant, and the distance traveled per hour is inversely proportional to time.
Suppose the ship sailed against the wind for x hours.
30×4/5x=30×(6-x)
4/5 times =6 times
9/5x=6
x= 10/3
30× 4/5×10/3 = 80km.
A: This ship should sail for 80 kilometers at most.
1 1. A car traveled from place A to place B in the first hour 1/7, and the second hour traveled more than the first hour 16 km. At this time, it is 94 kilometers away from B. How many kilometers is the expressway between A and B?
Analysis: "The second hour is 16km more than the first hour", which means that the second hour is 1/7 and 16km, and the first and second hours are (1/7+ 1/7) and
According to the above analysis:
(96+ 16)÷( 1- 1/7- 1/7)
= 1 12÷5/7
= 1 12×7/5
=156.8km.
A: The expressway between A and B is 156, which is 8 kilometers long.
Or use equations.
The road between Party A and Party B is x kilometers long.
( 1- 1/7- 1/7)x = 96+ 16
5/7x= 1 12
x= 156、8
A: The expressway between A and B is 156, which is 8 kilometers long.
Topic adaptation: If one of the conditions in this topic is changed to "it is 96 kilometers away from a certain place at this time", other conditions remain unchanged and the topic remains unchanged. How to answer?
12. A knitting group once used 30 people 10 to produce 1500 flower baskets. Now it has increased to 80 people. According to the original work efficiency, how many days does it take to produce 6000 flower baskets? (Answer in proportion)
Analysis: the title says "according to the original efficiency", which shows that the working efficiency of this textile group is certain. The work efficiency is certain, and the total amount of work is directly proportional to the working hours.
It takes x days.
1500:(30×50)=6000:(80×x)
1500×(80×x)=6000×(30×50)
x=6000×30×50÷80÷ 1500
x = 6000÷ 80
x=75
A: It takes 75 days.
13. There are two wheat fields in Hong Guang Farm, the first is 5.5 hectares, the second is 3.6 hectares, and the second is 18.2 tons. How many tons of wheat are harvested on average per hectare in these two wheat fields?
14. A car is driving in the mountainous area. It took three hours to climb the mountain, with an average speed of 30 kilometers per hour. On the same journey, it only took 2 hours to go down the mountain. Find the average speed of the car going up and down the mountain.
15. Party A and Party B walk in opposite directions from the same place at the same time. Party A travels every hour15km, and Party B travels every hour12km. How many kilometers are they apart in 4.5 hours? How many kilometers did A walk more than B?
16. The garment factory plans to make 1470 sets of clothes, which has been done for five days, with an average of 150 sets per day, and the remaining 4.5 days to complete. How many sets do you make on average every day?
17. Each set of children's clothing cloth is 2.5m, and each set of adult clothing cloth is 4m. Now we have to make 5 sets of children's clothes and 3 sets of adult clothes, and there are 30 meters of cloth. How much rice cloth can we leave? If each pair of trousers is made of cloth 1. 1 m, how many pairs of trousers can be made of the remaining cloth?
18. The supermarket launched the activity of "buy 5 get free 1" for mineral water. There are 48 people in a tour group. How many bottles of water do you need to buy if you want to give everyone a bottle of mineral water?
(Buy 5 to get 1 means that you only need to buy 5 bottles for 6 bottles of mineral water, and 48 has 8 6s, so you only need 8 5s. The answer is 40 bottles. )
19. The decimal part is two decimal places. Use rounding method to make it accurate to 0. 1, and its approximate value is 5.0. What is this two decimal places?
(Analysis: The required two decimal places are: 4.95, 4.96, 4.97, 4.98, 4.99, 5.00, 5.0 1, 5.02, 5.03 and 5.04.
20. A cuboid iron box with a square bottom will get a square with a side length of 40 cm if one side of it is unfolded. What is the volume of this iron box?
《 40÷4= 10 10× 10×40÷ 1000=4》
Respondents: cyg 2436- Senior Manager Level 71-1215:16.
Topic selection of Olympic mathematics in the fifth grade of primary school
fill-in-the-blank question
1. Calculation: 0.02+0.04+0.06+0.08+...+19.94+19.96+19.98 = _ _ _.
2./kloc-0 /×1+2× 2+3× 3+...1997×1998×1998 is _ _ _ _ _
3. A two-digit number, add a 0 between its two digits, which is 630 more than the original number. Such two digits are _ _ _ _ _.
At present, there are four RMB 1, two RMB 2 and three RMB 10. If you take at least 1 piece and at most 9 pieces, then * * * can be made into _ _ _ _ _ _.
5. A set of four digits, each digit is not 0 and different from each other, but the sum of all digits of each digit is 12. Put these four numbers in descending order, and the 25th place is _ _ _ _ _ _ _ _.
6. The big monkey gives the little monkey peaches. If each monkey gets 8 peaches, there are 10 peaches left. If each little monkey is divided into 9 peaches, then a little monkey will be divided into less than 9 peaches, but it can still be divided into peaches, small ones.
8. There is a residential building, and each family subscribes to two different newspapers. Residential buildings subscribe to three newspapers, including 34 Nantong Radio and Television Newspapers, 30 Yangzi Evening News and 22 newspaper abstracts. Therefore, the * * subscribing to Yangzi Evening News and Newspaper Digest has _ _ _ _ _.
9. Qiang Qiang and Fang Fang are running back and forth on the straight road of 120 meters. Qiang Qiang runs 2 meters per second and Fang Fang runs 3 meters per second. If they start from both ends at the same time, they * * * meet _ _ _ times in 15 minutes.
10. A workshop processed a batch of parts, and planned to process 48 parts a day, but actually processed one day more than planned 12 parts, which led to the completion of the task five days ahead of schedule. There are _ _ _ _ _ _ parts in this batch.
(Adapted from the 427 issue of "Decimal Newspaper")
1 1. The sum of the ages of Li, Sun and Wang this year is 1 13 years old. When Wang was 38 years old, Sun was twice as old as Li. When Li 17 years old, Wang was twice as old as Sun. Sun is _ _ _ _ _ _ _ _ years old this year.
(Decimal newspaper 492,98-9-18)
(Decimal Report 475)
13. There are 16 locks and 20 keys, of which 16 and 16 of 20 keys are paired one by one, but now the locks and keys are mixed together. Then, it takes at least _ _ _ _ times to ensure that the lock and key are paired.
(Decimal newspaper 457, adapted)
(adapted from decimal newspaper 475,98-4 98-4- 10/0)
15. Four students, A, B, C and D, participated in the math competition for primary school students in Nantong. Before the competition, three teachers made predictions:
A teacher said: C first, A second;
Another teacher said: B is the first and D is the fourth;
There is also a teacher: Ding comes second and C comes third.