Solve a few 6th grade math problems about circles.

The number stands for multiplication.

Circle area = square area 6*6

The radius of the garden is r, and the side of the square is a

There is a known 2*, a r=

Area ratio a*a

3) The square area is the largest when the circumference is equal. So it's 25 square meters.

In the third question, the first two specific numbers can be calculated by yourself.

Haha......

1. The area of the circle = square = square centimeter.

The area of the square = 6*6 = 36 square centimeters.

Therefore, choose B2 and set the perimeter to X.

Positive: circle = x 4*x*4 = x square 16: squared.

3. The square of (1) = 22/107 = again

2) = square of square = square meters.

3) The square of 20 4 = 25 square meters (because the circumference is the same, the area of the enclosed figure is the square).

Question 1: Choose A

Question 2: Choose D

The first sub-question in the third question: square meters.

Question 2: Square meters.

Question 3:

1,b because when the diameter of the circle is 2, the area of the circle is about and the area of the square is 4

2,d3,20 4 squared = 25 square meters (because the circumference is the same, the enclosed figure is the largest area of the square).

1. a 2. d

It's so simple.

According to the formula s=r

There is another question to know.

The radius of the great circle is 2 times the radius of the small circle, then the area of the great circle is 4 times the area of the small circle, and the area of the large circle is 12 square meters more than the area of the small circle.

It can be seen that the area of a small circle is 12 divided by 3 equal to 4 square meters.

Set the radius of the small circle.

x is the radius of the great circle.

2x(2x) squared - (x)squared =12

3x squared = 12

x square = 4

So the area of the small circle is equal to 4

Question 1. The distance pressed by one rotation of the wheel is equivalent to the circumference of the wheel, and the diameter of the wheel is known to be 66 cm, then the circumference of the wheel is equal to the diameter multiplied by the pi: 66 * cm).

After that, the circumference of the wheel is equal to the distance the wheel has been pressed in one revolution, and it is known that if the wheel has rotated for 100 cycles per minute, then the sum of the distance traveled by the wheel per minute is equal to centimeters multiplied by 100 cycles: centimeters.

It is also known that the total distance is 2000 meters, pay attention to the unit conversion, here it is replaced by centimeters, that is, 200000 centimeters, the speed is 20724 centimeters per minute, and the time is equal to the distance divided by the speed: 200000 20724, which is about 10 minutes.

Note: * equals the multiplier sign

Equal to the division sign, the last step no matter what the number calculated after the decimal point is, it is empty to do not use rounding, because it is counted as one minute, more than 9 minutes and one second, it will also be counted as 10 minutes.

Question 2. The length of the minute hand in the question is equivalent to the radius of a circle, which you can take a circular clock to look at, and after 30 minutes, the tip of the minute hand has traveled the distance in the circumference of the semicircle, and you can also take a look at the clock. In this way, the purpose of the first question is to find the circumference of the semicircle without including the bottom edge.

First of all, let's talk about the first question, first find the circumference of the circle, the radius multiplied by 2 times the pi: 20*2*cm, this is the circumference of the circle, the circumference of the semicircle and excluding the bottom edge is equivalent to dividing the circumference of the circle into two, that is, centimeters. The first question is solved, and the second question, 45 minutes, is equivalent to walking three-quarters of the circle, so multiply the circumference of the circle by three-quarters to get the result of the second question:

Centimeter. Note: The last 3 and 4 are equal to the score line, and the rest of the symbols are the same as in the first question.

Because the diameter of the great circle is the diagonal length of the square. The diameter of the small circle is the length of the sides of the square. The diameter of the minor circle is one-half of the root number of the diameter of the large circle.

Circle area formula s=pi*d 2 4. So the area ratio is the square of the diameter ratio. So the area of the small circle is half the area of the large circle.

The radius of the great circle is 1 2 of the diagonal of the square; s=root number under 2)*a 2) 2 ; a is the square side length.

The radius of the small circle is 1 2 for the square to become longers=

So the area of the minor circle is 1 2 of the area of the larger circle

If the diameter of the minor circle is 2a, then the diameter of the major circle is the diagonal length of the square, that is, (2 under the root number)*2a.

The area of the circle is pai*radius*radius.

The relationship between the area of the small circle pai*4*a*a and the area of the large circle is pai*8*a*a2.

Solution: Square of radius = diameter of a great circle = 4 Radius = 2 Square area = 4*2 = 8 1 4 Square area = 8 4 = 2 That is, the radius of the small circle squared = 2 So the area of the small circle = 2* (square centimeters) A... Hopefully, you can understand the effort Question 2 Using rotation, you can see that there are two triangles, i.e., a parallelogram, and the area of the shadow = 6*3=18

1. 1 The diameter of a wheel is 50cm, and the wheel rotates for one time, about forward ( m.

2 When the distance between the feet of the compass is 5 cm, draw the circumference of the circle as ( cm.

3 The radius of a circle is enlarged by a factor of 2, its circumference is enlarged by a factor of two, and the area is enlarged by a factor of two.

4 The outer diameter of a ring is 10 cm, the inner circle is 8 cm, and its area is ( cm2.

5.Bend a decimeter of wire into a circular ring (excluding the interface), the diameter of the ring is ( decimeter, the area is ( square decimeter.

6 The formula for calculating the circumference of a circle is: ( or (

The formula for calculating the area of a circle is: (

2. Judgment is true or false.

1. The diameter is always longer than the radius. （

2. The center of the circle determines the position of the circle, and the radius determines the size of the circle.

3. The area of a circle is equal to the area of a square, and their circumferences are also equal. (4. The circumference of a semicircle is half of the circumference of this circle.)

5. Of all the line segments with both ends on the circle, the diameter is the longest one.

3. Choice. 1. In the following figures, the axis of symmetry is the most (

a, square b, circle c, isosceles triangle 2, the minute hand of a clock is 10 cm long, from 2 o'clock to 4 o'clock, the minute hand has passed ( cm.

a、 b、 c、314

3. The circumference of a circle is decimeter, and its area is ( square decimeter.

a、 b、 c、314

4. Pi (

a, greater than b, equal to c, less than.

5. A semicircle, the radius is r, and its circumference is (

1.A circle is a circle with a radius of r = root number 2 + 1) and a circumference of l = 2 r

Bundle 4 turns is the length of 8 r 2

This is a problem of calculating the circumference and area of a circle.

1. The distance traveled by the tip of the minute hand is the circumference of the clock From the question, it can be seen that the radius is 30cm c= The area swept by the minute hand is the area of this circle (because the hour hand exactly turns on the clock surface) s=

2 The diameter is 8cm, the radius is 4cm, and the area is the pi multiplied by the radius squared.

3 Calculate the area swept by each range, which is closest to 314 square meters (the answer is 10cm).

4 This is the problem of circumference, you first have to calculate how many meters the wheel turns, and then multiply it by 50, and then you will solve it.

I hope you understand what I'm saying.

1: The minute hand of a clock is 30 cm long, and after 1 hour, how many centimeters does the tip of the minute hand travel? How big is the area swept by the minute hand?

The length of the sweep and the perimeter).

2: There is a circular pool with a diameter of 8m, how big is the area of this pool?

3: There is a circular lawn with an area of 314 square meters, and it is ready to be equipped with automatic rotary sprinkler irrigation. There are three types of devices with a range of 20m, 15m, and 10m, which do you think is the right choice? Where is it installed on the lawn?

314 100 = 10 10 So choose a 10m device.

4: A bicycle, its outer diameter of the wheel is 80cm, if the wheel turns an average of 50 times per minute, then how many meters can the bicycle travel per minute?

80cm = meters.

The hour is a circle, so it means to calculate the circumference of the circle, the circumference of the circle: 2 r=2*; The area swept is the area of the circle: s = r 2 = square centimeters.

m3According to the area of the circle s= r 2,314 = we get r = 10m. A 10m installation is installed in the center.

4.Circumference c=2 r=2* 50 laps is 50*

1. The minute hand travels a full circle in one hour, so the distance traveled by the tip of the minute hand is. The area swept is a square centimeter.

2. The floor area of the pool is square meters.

3. Choose a 10m device and install it in the center of the lawn.

4. The bicycle walks meters per minute hand.

1.The minute hand is circled in one hour, so the distance is the circumference = 2 r =, and the area swept is the area of the circle = r = 2826 square centimeters.

2.The diameter is 8m, the radius is 4m, and the area is r = square meter 3The area of the circle is 314 square meters, the area is equal to r, it can be calculated that the radius is 10m, the device with a range of 10m is selected, installed in the center of the circle.

4.Each revolution is the circumference, the circumference is 2 r=2*, and 50 revolutions per minute, then it is 50*circumference=12560cm=

1. The distance traveled by the wheel per revolution is the circumference of the wheel

cm) distance traveled per minute.

cm) 2000 meters = 200000 centimeters.

10 (minutes).

2.Circumference: 2-20 cm).

30 minutes 60 minutes = 1 2

cm) 45 minutes 60 minutes =

cm)3Is there a stake every 1 meter?

Circumference: m) root).

The unit of circumference of that semicircle is meters:m.

First, calculate the radius r of the circle, let the radius of the circle be x(m), and the diameter of the circle be 2x(m).

Equation: 2*

The solution is x=5 the area of the semicircle: 5 squared and 2=square meters.

Question 2: Actually, the diameter of this circle is the length of the sides of the square.

Side length a = root number 10 cm

The radius of the circle is one-half of the root number 10

The area of the circle: the square of the root number 10 (both 10) = square centimeters.

1.Let the radius of this semicircle be a

Then the perimeter c = diameter + arc length of the semicircle = 2a + 1 2 * 2a = 2a + a = (2+ )a

So the radius is m

So the area is 5*5* =25 = square meters.

r 2 is the square of r.

2.Let the radius be r, then the side length is 2r, so 2r*2r=10r 2=

So the area is r 2= square centimeters.

Circumference = circumference 2 + diameter = d 2 + d = (1 + 2) d take =

Rule. Circumference = (1 + 2) d = (1 + m).

then d = 10 meters.

Area = area of the circle 2=( d*d 4) 2=square meter) The diameter of the maximum circumscribed circle of the square is equal to the length of the sides of the square.

Then the diameter of the circle d = 10 (cm).

then the area of the circle = d*d 4 = square centimeters).

1) Set the diameter of the semicircle to x

x = 2570 414 2570 207 times.

2) 5 times 5 times.

First question:

The wheel is made in a circle according to the geometric nature of the circle: it is equal to the radius of the circle

When the wheels roll on flat ground, the axles are always on the plane of the same height, and the rider will not have the feeling of bumping up and down, which is very comfortable.

Second question:

Because the resistance should be minimized, the distance between the ground contact point and the axle should be equal at all times, so that the wheel is the garden, and the position where the axle should be installed in the center of the park ensures that the distance between the ground contact point and the axle is equal at all times.

Reason: The round wheel can roll drippingly, which is just a superficial phenomenon, and we must grasp the essence of the circle, conduct a scientific analysis of the circle, and find out the fundamental reason why the wheel is made into a circle.

What are the important properties of circles?

The outer circle is called the circumference, and the point where the compass is tied when the circle is drawn is called the center of the circle. Let's take a ruler and measure the distance from any point in the circumference to the center of the circle, they are all equal. This equal distance is called the radius. This is the importance of the circle.

If the wheel is made round and the axle is placed in the center of the circle, when the wheel rolls on the ground, the distance between the axle and the ground is always equal to the radius of the wheel. Therefore, the carriage mounted on the axle, and the people sitting in the carriage, will be smoothly pulled by the car. Suppose the wheel is broken, it is no longer round, and the rim is one piece higher and one piece lower, that is to say, the distance from the rim to the center of the wheel circle is not equal, then this kind of car must turn your head upside down.

Of course, there are other reasons why the wheels are round, for example: when something rolls on the ground, it is much less labor-saving than dragging on the ground, because the rolling friction resistance is smaller than the sliding friction resistance.

So, you must know why you use a compass when drawing circles. Because when the compass foot is opened, the distance between its feet is constant.

When did people come to know this property of the circle? Indeed, this was a long time ago. In the beginning, it was nature that inspired people to see how round the sun in the sky and the moon and a half moon were!

These objectively existing things give people the image of a circle. Gradually, the concept of a circle was born. People also began to learn to draw circles, but it was not easy to draw a very smooth circle.

After people knew that the distance from each point of the circle to a fixed point (circle center) was equal from production practice, they invented the compass to draw a circle.