Analysis: If the cube is cut into the largest cylinder, the diameter and height of the bottom of the cylinder are the sides of the cube. Let the side length of the cube be a (a(a>0), then the volume of the cube is a? , the volume of the cylinder is π×(a÷2)? ×a=π÷4×a？ It shows that the volume of a cylinder is π÷4 of the volume of a cube.
Answer: 94.2÷(3. 14÷4)= 1
There is a cylindrical glass with a bottom diameter of 20cm and some water. It is known that the water level in the glass is 3 cm away from the mouth of the glass. If a conical lead cone is immersed in a cup, water will overflow 20 ml. Find the volume of the lead cone.
Analysis: the volume of the lead cone is equal to the volume of a cylinder with a bottom diameter of 20cm and a height of 3cm, plus the volume of water overflowing from the cup, regardless of the shape of the lead cone.
Answer: 3. 14×(20÷2)? ×3+20=
3. The volume of a cube is 225cm? The radius and height of the bottom of the cone are equal to the side length of the cube. Find the volume of this cone.
Analysis: let the side length of the cube be a, then a? =25cm？ . According to the relationship between the cone and the cube, the volume of the cone is 1/3πa? ×a= 1/3πa？
Answer: 1/3×3. 14×225=
4. Both master and apprentice produce the same parts. It is known that the master produces 1/3 more parts than the apprentice, but the apprentice spends 1/4 less time than the master. Seek the efficiency ratio of mentoring.
Analysis: If the total labor of the apprentice is regarded as a whole, the total labor of the master is (1+ 1/3), and the labor time of the master is regarded as a whole, and the labor time of the land is (1- 1/4).
Answer: 1: 1
A hunting dog found a running rabbit 8 meters away from it and immediately caught up with it. It is known that the distance that a hound runs two steps is the distance that a rabbit runs five steps, but the rabbit is fast, and the hound can only run three steps when the rabbit runs five steps. How many meters does the hound have to run to catch up with the rabbit?
Analysis: the hound runs 2 steps and the rabbit runs 5 steps, so the hound's step: the rabbit's step = 1/2: 1/4 = 5: 2. The rabbit runs five steps, and the hound can run three steps, so the number of steps the hound runs: the number of steps the rabbit runs =3:5. Therefore, the distance that hounds run: the distance that rabbits run = (5× 3): (2× 5) = 3: 2.
Answer:1/2:1/5 (5× 3): (2× 5) = 3: 2.
x:(x-80)=3:2
6. It takes a ship eight hours to sail between Port A and Port B at a time. Because of the smooth sailing, the journey from port A to port B is 45km, and the return journey is 35km. How many kilometers is it between Port A and Port B?
Analysis: Because the round-trip distance is equal, the speed is inversely proportional to the time. 45:35=9:7, so the return time ratio is 7:9.
Answer: 45:35=9:7
45× (8× 7/16) = 315/2km.
7. It takes 8 hours for Party A to complete a batch of parts alone. Assuming that the efficiency ratio between Party A and Party B is 4:3, how long will it take for Party B to complete it alone?
Analysis: If the total number of these parts is regarded as a unit, the work efficiency of Party A is 1/8, and if it takes X hours for Party B to complete it alone, the work efficiency is 1/x. The work efficiency ratio of Party A and Party B is 1/8: 1/x, which is 4:3.
Answer: 1/8: 1x=4:3.
8. If a batch of parts is processed in the first workshop of accessories and 30 parts are processed every hour, it can be completed 10 hour in advance. If processing 20 parts per hour can be completed 6 hours in advance, how many parts are there in this batch?
Analysis: The total number of these parts is fixed, so the number of parts processed per hour is inversely proportional to the processing time.
Answer: 30× (x-10) = 20× (x-6) x =18.
Total number of parts: 30× (18-10) =1
9. Li Ming poured himself a full glass of coke and a full glass of juice from the same cup. Li Mingxian drank half a cup of coke, and after his mother took a sip, he left two-thirds cups of juice. Then Li Ming filled his mother's cup with coke in his own. After fully mixing, his mother filled Li Ming's cup with the drinks in his own, and finally they both drank all the drinks in the cup. How many cokes did Li Ming drink?
Analysis: The cola that Li Ming drank included half a cup he drank for the first time, the one left after pouring it to his mother, and the cola that her mother poured into Li Ming's cup.
Answer: Li Ming drank 1/2 cups for the first time, and there were1-1/2 cups left.
The coke poured into mom's cup is 1-2/3= 1/3 (cup), and the rest is1/2-1/3 =1/6 (cup).
The coke left after mom poured it back into Li Ming's cup is1/3x1/6 =118 (cup).
Li Ming drank1-118 =17/18 (cup).