"Area of ​​a Circle" Circle PPT teaching courseware

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"Area of ​​a Circle" Circle PPT teaching courseware

Part One: Introduction to the topic

8 yuan per square meter of turf. How many square meters does this circular lawn cover?

What mathematical questions can be asked based on the information in the figure?

Area of ​​a circle PPT, part 2 content: new teaching knowledge

Divide one into several (even-numbered) equal parts, cut them and put these small pieces of paper that are similar to isosceles triangles together, and the resulting figure will be close to a rectangle.

【in conclusion】

The length of the rectangle ≈ half the circumference of the circle The width of the rectangle ≈ the radius of the circle

Area of ​​a rectangle = length × width Area of ​​a circle = half of the circumference × radius

Area of ​​a circle PPT, part three: application practice

Example 1: There is a circular lawn with a diameter of 20 meters, and each square meter of turf costs 8 yuan. How much does it cost to lay full sod?

Area of ​​the circle: S＝πr² Radius: r=20÷2=10 (meters)

Lawn area: 3.14×102=314 (square meters)

Total required: 314×8=2512 (yuan)

[Analysis] First, you should find out the area of ​​the circular lawn, and then multiply the area by the unit price to get the total cost of covering the lawn.

Area of ​​a circle PPT, part 4 content: new teaching knowledge

Do you know what the shapes above are? Can you give any other examples?

What is a ring?

Two concentric circles with unequal radii, the part where the area of ​​the larger circle is greater than the area of ​​the smaller circle is the ring.

What is the area of ​​the ring?

Circular area = outer circle area – inner circle area

S=πR²�πr² S=π(R²�r²)

Area of ​​a circle PPT, part 5: expanded application

1. The radius of the large circle in the picture is equal to the diameter of the small circle. Find the area of ​​the shaded part.

Area of ​​the great circle: S＝πr²＝3.14 ×6²= 113.04 cm²

Small circle radius: r＝6÷2＝3 cm

Area of ​​the small circle: S＝πr²＝ 3.14×3² = 28.26 cm²

Shaded area: 113.04 – 28.26 = 84.78 cm²

2. A sports field (as shown in the picture) has semicircles at both ends and a rectangle in the middle. How many meters is the circumference of this sports field? How many square meters is the area?

Circumference of two semicircles: 2×3.14×32 = 200.96 (meters)

The length of the two long sides of the rectangle: 100×2 = 200 (meters)

Circumference of sports field: 200.96+200 = 400.96 (meters)

Area of ​​a circle PPT, part 6 content: knowledge sorting

Knowledge point 1: Area of ​​a circle

π≈3.14 S＝πr²

Example: The school builds a circular flower bed at a cost of 50 yuan per square meter. After the flower bed was repaired, the school paid the construction team 700 yuan, and the construction team found 72 yuan. Do you know the radius of this circular flower bed?

Actual sharing: 700-72=628 (yuan)

Flower bed area: 628÷50=12.56 (square meters)

S=πr²=12.56

r²＝12.56 ÷3.14＝4 r＝2 (meter)

[Analysis] To determine the radius of a circular flower bed, you must first know its area. From the wages paid, we can know how many square meters of flower beds were built, and then find the radius of the flower beds from the area of ​​the flower beds.

Knowledge point 2: Area of ​​the ring

Ring area = outer circle area – inner circle area

That is: S=πR²�πr² or S=π(R²�r²)

Example: There is a circular flower bed in Xingfu Community with a diameter of 6 meters. There is a 2-meter wide path paved with fitness stones around it. What is the area of ​​this path in square meters?

Inner circle radius: 6÷2=3 (meters)

Outer circle radius: 3+2= 5 (meters)

Path area: 3.14×5²-3.14×3²=50.24 (square meters)

[Analysis] Finding the area of ​​this path is actually finding the area of ​​the circle. It can be calculated according to the formula of ring = area of ​​outer circle - area of ​​inner circle.

Area of ​​a circle PPT, Part 7: Classroom exercises

1. Fill in the blanks

(1) ( ) puts forward this great mathematical idea: "If you cut too thin, you will lose little. If you cut it again and again until it cannot be cut, then it will be integrated with the circle and nothing will be lost." This great mathematical idea.

(2) Divide a circle into several equal parts, and then cut it to form a figure similar to ( ). The length of this ( ) is equal to the circle ( ), and the width is the circle ( ).

(3) The radius of a circle is 1 meter, the diameter of the circle is ( ) meters, the circumference is ( ) meters, and the area is ( ) square meters.

(4) For a ring, the circumference of the inner circle is 9.42 cm, the width of the ring is 2 cm, the radius of the inner circle is ( ) cm, and the radius of the outer circle is ( ) cm.

(5) A rectangular piece of paper is 6 cm long and 4 cm wide. Cut it into the largest circle. The radius of this circle is ( ) cm, the circumference is ( ) cm, and the area is ( ) square centimeters.

(6) The radius of the circle is expanded by 2 times, the circumference is expanded by ( ) times, and the area is expanded by ( ) times.

2. Judgment

(1) Two circles with equal diameters must have equal areas. ( )

(2) The radius of the circle is 3 cm, and its circumference and area are equal. ( )

(3) Two semicircles can be combined into a full circle. ( )

(4) The longer the circumference of a circle, the longer the radius, and the larger the area. ( )

3. Select

(1) Among rectangles, squares, triangles and circles with equal perimeters, which one has the largest area? ( )

A. Rectangle B. Square C. Triangle D. Circle

(2) When the radius of a circle increases from 1 cm to 2 cm, how many square centimeters does the area of ​​the circle increase? ( )

A. 1 B. 2 C. 3 D. 3π

(3) If the diameter ratio of the two circles A and B is 2:1, what is the ratio of their areas? ( )

A. 2 : 4 B. 4 : 1 C. 1 : 2 D. 1 : 4

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For more information about the "Area of ​​a Circle" PPT courseware, please click on the Circle PPT Area of ​​a Circle PPT tab.

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Update Time: 2024-07-05

This template belongs to Mathematics courseware People's Education Press Sixth Grade Mathematics Volume 1 industry PPT template

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