"Application of linear equations of one variable" PPT courseware 8

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"Application of linear equations of one variable" PPT courseware 8

The general process of using equations to solve practical problems is:

1. Review the question: analyze the meaning of the question and find out the quantities and their relationships in the question;

2. Set the element: Choose an appropriate unknown number to represent it with a letter

(for example x); other quantities are expressed by algebraic expressions containing x

3. List equations: List equations based on equality relationships;

4. Solve equations: find the value of the unknown;

5. Check: Check whether the obtained value is correct and consistent with the actual situation, and write the answer.

Yi Yi Yi

Several important calculation formulas for perimeter, area, and volume that we learned in elementary school

Perimeter of rectangle: C=2(a+b)

The area of ​​the trapezoid: S=(a+b)×h÷2

Volume of cylinder: V=sh=πr²h

Volume of cuboid: V=sh=abh

Think about it: Please indicate which quantities changed and which quantities remained the same during the following process?

1. Pour a small cup of water into another large cup;

Solution: The bottom area and height of water have changed, but the volume of water remains unchanged.

2. Use a 15cm long wire to form a triangle, and then surround it into a rectangle;

Solution: The area of ​​the enclosed figure has changed, but the length of the wire remains unchanged.

3. Use a piece of plasticine to first make a cube, and then change it into a ball.

Solution: Shape changes but volume remains unchanged

Example 1: The base of a monument building is square, and granite is paved around it to form a square frame with a width of 3.2 meters (the shaded part in the picture). It is known that exactly 144 pieces with a side length of 0.8 were used to lay this frame. A square granite of 1.5 meters (joints are ignored), how many meters is the side length of the base of the monument?

1. In the title, "The base of the monument is square", which square is it referring to?

2. “Form a square border with a width of 3.2 meters.” Which section does the 3.2-meter border refer to?

3. The area of ​​the shaded part in the picture is paved with 144 square granite stones with a side length of 0.8 meters. How do you find the area of ​​the shaded part?

4. As shown in the figure, if x is used to represent the side length of the blank square in the middle, how to use an algebraic expression containing x to represent the area of ​​the shaded part? How many methods do you have?

5. What is the equivalence relationship in this question?

6. Please list the solution to the equation (can you list other equations?)

There is a cylinder with a base diameter of 20cm and a height of 9cm. The worker uncle wants to forge it into a cylinder with a base diameter of 10cm. The worker uncle wants to know how high the forged cylinder will be? Can you tell him?

1. What is the equivalence relationship in this question?

The volume of the cylinder before forging = the volume of the cylinder after forging

2. How to formulate an equation based on this equivalence relationship?

Solution: Suppose the height of the cylinder after forging is x centimeters. According to the meaning of the question, we get

π×(20/2)²×9=π×(10/2)²×x

Solving this equation, we get x=36

Answer: The height of the cylinder after forging is 36 cm

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Update Time: 2024-11-02

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