However, don't solve the first problem.
But let me show you the process.
Analysis: the figure obtained by one revolution is the figure with the bottom of two cones close to the bottom.
Solution: The rotating body consists of two cones, with a total height of 5cm and the same bottom surface.
Let the radius of the cone bottom be x, and X. 1/2*3*4= 1/2*5X can be obtained by equal product method.
X= 12/5=2.4 (cm). The volume of the rotator = 1/3*π2.4? *5=9.6π(cm？ )。
2. The topic should be like this: A father, before he died, told his son to divide the property like this: the first son got 100 kronor, one tenth of the remaining property; The second son gets 200 crowns and one tenth of the rest of the property; The third son gets 300 crowns and one tenth of the remaining property; The fourth son gets 400 crowns and one tenth of the remaining property ... so that each son gets the same property. Q: How many sons does this father have? How much property does each son get? How much property did father leave?
Solution: The problem of Euler's legacy is a problem in Euler's famous mathematical work Fundamentals of Algebra. The topic is this: A father told his son before he died to divide the property like this: the first son got 100 kronor, one tenth of the remaining property; The second son gets 2OO kronor and one tenth of the remaining property; The third son gets 300 crowns and one tenth of the remaining property; The fourth son gets 400 crowns and one tenth of the remaining property ... so that each son gets the same property. Q: How many sons does this father have? How much property does each son get? How much property did father leave?
We shouldn't be frightened by such a long topic. In fact, as long as we grasp the key points of the topic, calculate from the back to the front, and use the relevant knowledge of score application, we can easily solve it.
We might as well assume that this father has n sons, the last son is the nth son, and the penultimate son is the (n- 1) th son.
Through analysis, we can know that:
The property jointly owned by the first son =1oox1+110 of the remaining property;
The property jointly owned by the second son =100× 2+110 of the remaining property;
The property share of the third son =1oo× 3+110 of the remaining property;
The (n- 1) joint property =100× (n-1)+10 of the remaining property;
The property jointly owned by the nth son is 100n.
Because each son gets the same amount of property,
That is,100× (n-1)+110 =100n of the remaining property,
Therefore, when the (n- 1) th son took 100× (n- 1) th crown,
110 of the remaining property is100n-100× (n-1) =100 kronor.
Then, the remaining property is100110 =1000 kronor.
The last son got: 1000- 100 = 900 kronor.
It can be concluded that this father has (9OO÷ 100)= 9 sons.
* * * Leave the property 9OO× 9 = 8 100 kronor.
There are 45 students in one class, among whom 25 study piano, 35 computer, 37 art and 40 Olympic Mathematics. How many students in this class have learned at least the above four contents?
Solution: There are 28+40=68 people who study computers and Olympiad.
Both Olympics and computers are 68-45=23 (people);
Similarly, those who study both art and piano are (37+35)-45=27 (people);
So: at least (23+27)-45=5 (people) learn all four;