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Proportional math diary
February 10 Wednesday sunny.

Compare the scores by division.

It is sunny today. I was reading Mathematical Olympiad in Primary School at home, and suddenly I found such a problem: compare11111,1 165538. Suddenly, I became interested and took a pen and "brushed" it on the toilet paper. Soon, I found a solution Is to turn these two false scores into fractions and then use the law of fractions. The smaller the denominator, the greater the score. Solve111111

It will be fine on Friday, February 12.

Today, I saw such a problem in the training of Mathematics 1+2. A cubic casting with a bottom area of 648 square centimeters, what is the remaining three-dimensional graphic area after removing the largest cylinder and taking the opposite side as the bottom?

Seeing this topic, I was very confused and thought: just say a bottom area, how to do it? My mother sitting in the chair looked at it, smiled at me and said, "Hum, she can't even do this problem."

I know my mother used the goad method, in order to irritate my competitive spirit and let me finish this problem. In order to make my mother think that her provocation was successful, I crustily skin of head did it, but I couldn't figure it out. But I'm not discouraged. I persisted and finally succeeded.

According to the drawing (to be drawn), it can be found that when a cylinder is cut off, a hole with the same size as the original cylinder will come out. Although the volume of the hole is the same as that of the cylinder, their surface areas are not the same, but the areas of the two bottoms are smaller than that of the original cylinder.

Therefore, the remaining graphic area should be equal to the area of the six faces of the cube minus the two bottom faces of the cylinder+the side faces of the cylinder.

The formula is 628× 6-628× 3.14 ÷ 4× 2+628× 3.14.

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February 14 Saturday sunny.

Today is another sunny day. I was wandering in the street when I suddenly saw a lot of people gathered not far away. I ran for a year, and the result was a prize-winning game. "Hum, what's fun about winning the prize?" I was bored when the person next to me quickly said, "It's not fun to grab the prize, but there is a big prize that can attract people." I asked eagerly, "What is it!" "50 yuan money." The man with big eyes said. I'm very excited to hear that. "I have to try anything for such an attractive prize." Then I asked the shopkeeper how to grasp the rules. The shopkeeper said, "This is 24 Mahjong, and it says 12 5, 12 10. You can only catch 12 mahjong at a time. If the total number of 12 mahjong targets is 60, then you can win the 50 yuan Prize. " Without rolling up my sleeves, I took out 5 yuan money from my pocket and gave it to the shopkeeper.

Although I won 10 times, I still didn't win the grand prize.

When I got home, I thought about it and felt something was wrong. I think, to get 60 points, all 12 mahjong should be marked with 5. In the best case, the first 1 second catch 1 5, the second catch of two 5 s and the third catch of three 5 s will cost at least 6 yuan money. But what if the target number of mahjong is 10 or the sum of the two is the same, how many times will it cost?

Finally, after some consideration, I finally figured it out. I rushed to the street to get even with it, but it had disappeared without a trace.

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It will be fine on Monday, February 16.

Title: There are two candles with different thicknesses. A thin candle is twice as long as a thick candle. It takes 1 hour to light a thin candle and 2 hours to light a thick candle. Once there was a power failure, two used candles were lit at the same time. When the phone call came in, I found that the remaining length of the two candles was the same. How long was the power outage?

Solution: If the candle length is 1 and the burning speed is (1)1÷ 2 =1/2 (2) 2 ÷1= 2, the formula is: 65438.

Solution: Set the power outage time as x hours.

1— 1/2X=2—2X

X=2/3

A: The power outage time is 2/3 hours.

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It will be fine on Wednesday, February 18.

I saw such a problem in the "two-color class for primary school students" this afternoon.

The bottom radius of the cone is 8 decimeters, and the ratio of height to bottom radius is 3: 2. What is the volume of this cone?

Analysis: This is an application problem that combines the application problem with the cone problem in proportion. To calculate the volume of a cone, you need to know the bottom area and height of the cone. The topic is about the radius of the bottom surface, so we can find the bottom area, but we don't know the height. You can find it according to a condition, and convert the ratio into a number that accounts for a fraction of the known number, so that you can know that the height accounts for 3/2 of the radius of the bottom surface. After calculating the height, calculate the volume of the cone according to "V=SH÷3".