If the height of a cone does not change and the radius of its bottom increases by one third, how much does the volume increase? Don't be wrong,

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• 1. Fill in 1 / 2, 1 / 3, 1 / 6 in each formula to make the equation hold. (fraction + fraction) / fraction = 1
• 2. First press 3:1 to enlarge, then press 1:2 to reduce. What's the current area? What's the formula First press 3:1 to enlarge, then press 1:2 to reduce. What is the area now? What's the formula
• 3. 1.25 times 0.8 times 4 times 2.5 (simple formula)
• 4. Mathematics in the newspaper Specify an operation, a * b = AB / A + B, and calculate the value of 2 * (- 3) 2 * (- 3) = 6. I can do that, too. But the front a * b = AB / A + B,
• 5. We define a * b = AB-1 and calculate the value of 5 / 3 * 2=_________
• 6. There is a mathematical operation symbol "0", which makes the following formula true: 12023 = 36, 45079 = 1145, 56017 = 642. Find the value of 311045
• 7. There is a mathematical operation symbol "0", which makes the following formula true: 12023 = 36, 45079 = 1145, 56017 = 642. Find the value of 311045
• 8. Ask: there is a mathematical symbol *, so that the following formula holds: 2 * 4 = 8,5 * 3 = 13,3 * 5 = 11,9 * 7 = 25, then 7 * 3 =?
• 9. The number of a regularly arranged column: - 1,3, - 5,7, - 9,... What formula do you think can be used to express each of its terms?
• 10. 1 + 2 = 3 = 1 * 3 4 + 4 = 8 = 2 * 4 9 + 6 = 15 = 3 * 5 16 + 8 = 24 = 4 * 6 the law is expressed by the formula containing n
• 11. 6 is a fraction of 3
• 12. A formula for finding the fraction of one number to another The machinery factory produced a batch of machines, 20 in the first day, and 25% more in the second day than in the first day. The number of machines produced in the two days is exactly the same as that of this batch of machines 37.5%. How many machines are there in this batch?
• 13. It is known that 5 / 6 = 1 / 2 + 1 / 3, 7 / 12 = 1 / 3 + 1 / 4, 9 / 20 = + 1 / 4 + 1 / 5 1 + 2 1-6 5 + 12 7-20 9 + 30 11-42 13 Let's say what we mean! (yes, there is a reward)
• 14. 1 / 2 = 1-1 / 2, 1 / 6 = 1 / 2-1 / 3, 1 / 12 = 1 / 3-1 / 4. According to the above rule, calculate the following questions: 1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30
• 15. 1 / 2 = 1-2 / 1, 1 / 6 = 1 / 2-3 / 1, 1 / 12 = 1 / 3-4 / 1... According to the above rules, calculate the following question: 1 / 2 + 1 / 6 +1 in 12 + 1 in 20 + 1 in 30
• 16. 1 / 2 = 1-1 / 2, 1 / 6 = 1 / 2-1 / 3, 1 / 12 = 1 / 3-1 / 4
• 17. Specify a kind of operation: a * b = (a + 5 / 2) × (B-3 / 4) △ B, try to calculate 1 / 2 * 5 / 4
• 18. When a = 2 and B = 3, calculate the values of (a + b) 2 - (a-b) 2 and 4AB respectively, and find out what law (expressed by the formula containing a and b)
• 19. S = 1 + 2 ^ - 1 + 2 ^ - 2 + 2 ^ - 3 + +2 ^ - 2010, please calculate the formula on the right to get the value of S, (hint: multiply by 2 on both sides of the equation) do you see the law?
• 20. Observe the following formula: 1 ^ 2 + (1 * 2) ^ 2 + 2 ^ 2 = (1 * 2 + 1) ^ 2 ^ 2 + (2 * 3) ^ 2 + 3 ^ 2 = (3 * 2 + 1) ^ 2 ^ 2 + (3 * 4) ^ 2 + 4 ^ 2 = (3 * 4 + 1) ^ 2 Observe the following rules 1^2+(1*2)^2+2^2=(1*2+1)^2 2^2+(2*3)^2+3^2=(3*2+1)^2 3^2+(3*4)^2+4^2=(3*4+1)^2 ① Write the 2011 formula ② Write the formula on line N and prove your conclusion