First, the circle.

Basic knowledge of circle: letter diameter =d letter radius = R.

The circumference of a circle is represented by letters =C=πd or c = 2 π r.

The area of a circle is represented by letters: s=πr? . π=3. 14

1. Draw a circle with a perimeter of 12.56 cm, mark the center and radius with letters, and then calculate the area of the circle.

Area: 12.56/3. 14/2 = 2 (cm) 2 * 2 * 3. 14 = 12.56 (cm2).

A: The area is 12.56 cm.

There is a circular lawn in the school. Its diameter is 30 meters. What is the area of this lawn? If you put a pot of chrysanthemums every 1.57 meters around the lawn, how many pots of chrysanthemums should you prepare?

30/2= 15 (cm)15 *15 * 3.14 = 706.5 (m) 706.5/ 1.57=40 (basin)

Answer: The area is 706.5 meters, and 40 pots of chrysanthemums should be prepared.

3. The diameter of the circular flower bed is 10 cm, and there are 2-meter-wide paths around it. What is the area of this path?

10/2 = 5cm 5+2 = 7cm.

Square difference solution: S=π(R? -r？ )

=3. 14*(7? - 5? )

=3. 14*24

=75.36 cm

A: The area of this path is 75.36 cm.

The hour hand of the big clock is 0.3 meters long. How many meters has the tip of this hour hand traveled in 1 day? How many square meters is the sweeping area?

0.3*2*3. 14= 1.884 (m2)

A: I walked 1.884 meters in one day. The sweeping area is 0.2826 square meters.

5. The range of automatic rotary sprinkler irrigation device on the park lawn is 10 meter. How wide can it spray irrigation?

10 *10 * 3.14 = 314 (square meter)

A: He can spray irrigation on an area of 3 14 square meters.

6. There is a ring. The circumference of the inner circle is 3 1.4 cm, the circumference of the outer circle is 62.8 cm, and what is the width of the ring?

3 1.4/3. 14/2=5 (cm) 62.8/3. 14/2= 10 (cm)

10-5 = 5cm

A: The width of the ring is 5 cm.

7. Xiaodong has a bike. The diameter of the wheel is about 66 cm. If the average speed is 100 laps per minute, then the distance from home to school is 4 144.8 meters. How many minutes will it take?

66*3. 14=207.24 (cm) 207.24* 100=20724 (cm)

=207.24 (m) 4 144.8/207.24=20 (min)

A: It will take 20 minutes.

8. For a round bottom boiler, the circumference of the bottom circle is 1.57m, and what is the bottom area? (Figures shall be kept to two decimal places)

1.57/3. 14/2 = 0.25(m)0.25 * 0.25 * 3. 14 = 0. 19625(m？ )

0.20 square meters

A: The building area is 0.2 square meters.

Second, the percentage

1, the original price of a commodity is 20% less than the current price, and the current price is 1028 yuan. What is the original price?

1028 * (1-20%) = 822.4 (yuan)

A: The original price is 822.4 yuan.

2. A factory invested 320,000 yuan to build a new production workshop, 80,000 less than planned, and what percentage is less than planned?

8/32* 100%=25%

25% less than planned.

There was a bumper harvest of litchi in Xixiang this year, with the output reaching 36,000 tons, an increase of 20% over last year. What was the yield of litchi in Xixiang last year?

3.6/( 1+20%)=3 (ton)

A: The output is 3 tons.

4. To build a highway, Team A built 60% of the total length, Team B built 30% of the total length, and Team A built 27 kilometers more than Team B ... How many kilometers is this highway?

27/(60%-30%)=90 (ton)

Answer; This road weighs 90 tons.

5. Tickets for children's playgrounds were originally 20% off for each 30 yuan during the Spring Festival. How much can Mr. Liu's family of three save by going to the playground to buy tickets?

30*3*80%=72 (yuan) 30*3-72= 18 (yuan)

A: A * * * can save 18 yuan.

6. The current price of a TV set is 6000 yuan, and the profit is 20%. What is the purchase price of this TV set?

6000*( 1-20%)=4800 (yuan)

The purchase price of this TV is 4800 yuan.

7. Miss Li deposited 2000 yuan in the bank for five years, with an annual interest rate of 4. 14%. How much money can Miss Li get back when it expires? (Interest tax is 5%. )

2000+2000 * 5 * 4.14% * (1-5%) = 2393.3 (yuan)

8. How many tons of wheat is needed to grind 13.6 tons of flour with a flour yield of 85%?

13.6/85%= 16 (ton)

This requires 16 tons of wheat.

9. The clothing store bought two clothes at the same time, each of which earned 120 yuan, but one of them earned 20% and the other lost 20%. Did the two clothes sold by the clothing store make money or lose money?

120 ÷ (1+20%) =100 (yuan)

100+ 150=250 yuan 120×2=240 yuan

250-240= 10 (yuan)

Answer: compensation 10 yuan.

Three. Ratio and proportion

1. Make a 600g bean paste bun with the ratio of flour, red beans and sugar of 3:2: 1. How many grams of flour, red beans and sugar do you need?

3+2+ 1 = 6 600 * = 100(g)600 *？ =200 (grams)

600* =300 (g)

Answer: 300 grams of flour, 200 grams of red beans, sugar 100 grams.

2. The circumference of a rectangle is 24cm, and the length-width ratio is 2: 1. How many square centimeters is the area of this rectangle?

24/2= 12 (cm) 2+ 1=3 (cm) 12* =4 (cm)

12*) 4*8=32 (cm)

A: The area is 32 cm.

3. The total length of a cuboid is 96 cm, the height is 4 cm, and the length-width ratio is 3 ∶2. What is the volume of this cuboid?

96/4 = 24cm3+2 = 5cm 24-4 = 20cm

20 * = 12(cm)20 * = 8(cm)8 * 12 * 4 = 384(cm？ )

The volume of this rectangle is 384 cm? .

4. Two engineering teams, Team A and Team B, built a 360m road, and the length ratio of Team A and Team B was 5: 4. How many meters did Team A build more than Team B?

5+4 = 9 360 * = 200m 360 * =160m

200- 160=40 (m)

A: it was repaired for 40 meters.

5. There are 42 computer interest groups in a school. The ratio of male to female is 4: 3. How many boys are there?

6. There are two baskets of fruit. The fruit in the first basket weighs 32 kilograms. After taking out 20% from the second basket, the weight ratio of the two baskets of fruits is 4:3. How many kilograms were there in the original two baskets of fruit?

Solution: The fruit in the original box B is X kilograms. After taking out 20%, the fruit in the second basket is (1-20%)X kg, that is, 0.8X kg.

32:0.8X=4:3

Solution: x=30 kg.

30+32 = 62kg

A: * * * There are 62 kilograms.

7. The ratio of the three internal angles of a triangle is 2:3:4. What are the degrees of these three internal angles?

2+3+4=9 180* =40 180* =60

180* =80

A: They are 40, 60 and 80 respectively.

8. A naughty family of three and a smiling family of four go to a restaurant for dinner, with a total meal fee of ***280 yuan. The two families decided to share the cost of meals according to the number of people. How much does each family pay?

3+4=7 280* = 120 (yuan) 280* = 160 (yuan)

A: The naughty family made friends 120 yuan, and the smiling family made friends 160 yuan.

10. In the "Learn from Lei Feng" activity, students in grade five and grade six did 80 good deeds on average, and the ratio of the number of good deeds in grade five and grade six was 3︰5. How many good deeds did the sixth graders do?

80*2= 160 (a) 3+5=8 160* =60 (a)

160* = 100 (piece)

A: The fifth grade made 60 yuan and the sixth grade made 100 yuan.

For your reference, I may have done something wrong. After all, I'm only in the sixth grade. thank you