Do two circles have the same perimeter and the same area?

Do two circles have the same perimeter and the same area?

yes

The circumference of a semicircle is 25.7. Find its area

The circumference of the semicircle includes half of the circumference plus a diameter, so the total should be 3.14 / 2 + 1 = 2.57 times of the diameter
So the diameter of this circle is 25.7 / 2.57 = 10,
10/2=5
The area is 3.14 * 5 * 5 / 2 = 78.5 / 2 = 39.25

Primary school mathematics problem: cut the largest square from a piece of paper. The circumference of the circle is known to be 25.14 cm. How about the area of the square?

The circumference of the circle should be 25.12
Because the circumference of the circle is 25.12cm, its radius is 25.12g6.28 = 4cm
The square can be divided into four right triangles, the bottom and height of which are the radius of the circle
So the area of this square should be 4 * 4 * 4 / 2 = 32 square centimeters

There are rays OC and od in ∠ AOB, ∠ AOD = 35 ° and ∠ cob = 44 ° and ∠ AOC = 2 / 3 ∠ DOB. Calculate the degree of ∠ AOB

∠AOC=2/3∠DOB
∠DOB-∠AOC=∠DOB-2/3∠DOB=∠DOB/3
∠AOD=∠AOC+∠COD=35° 1
∠COB=∠COD+∠DOB=44° 2
2-1
∠DOB-∠AOC=∠DOB/3=44°-35°=9°
∠DOB=27°
∠AOC=27°-9°=18°
Then ∠ cod = 44 ° - 27 ° = 17 °
1 + 2
∠AOD+∠COB=∠AOD+2∠COD+∠DOB=∠AOB+∠COD=44°+35°=79°
∠AOB=79°-17°=62°

As shown in Figure 6, it is known that O is a point on the straight line AB, OC and od are two rays with o as the end point, OE bisects ∠ AOC, ∠ BOC: ∠ AOE: ∠ AOD = 2:5:8,
Find the degree of ∠ BOD

Solution to AOC of known OE bisector angle
Then angle AOE = angle Coe
Because ∠ AOE + ∠ eco + cob = 180 degree
And because ∠ cob; ∠ AOE = 2; 5
So 2A + 5A + 5A = 180
12a=180
a=1 5
Then ∠ AOD = 15 × 8 = 120 degree
Therefore, DOB = 180 minus 120
=60°

As shown in the figure, for the eight rays OA, ob, OC, OD, OE, of, og, oh with common endpoints in the plane, the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are written on the rays in a counter clockwise direction starting from the ray OA According to this rule, the number 2010 is in the ray ()
A. OA B. ob C. OC D. of

According to the meaning of the question, every 8 numbers is a cycle. Because 2010 △ 8 = 251 more than 2, the number 2010 should be on the ray ob

As shown in the figure, it is known that OA ⊥ ob, ∠ 1 and ∠ 2 complement each other, and the verification is OC ⊥ OD

It is proved that ∵ 1 and ∵ 2 complement each other, ∵ 1 + 2 = 180 °, ∵ OA ⊥ ob, ∵ AOB = 90 °, ∵ cod = 360 ° - (∵ 1 + 2) - ∵ AOB = 360 ° - 180 ° - 90 ° = 90 ° and ∵ OC ⊥ OD

It is known that the radius of the sector OAB is 3, the central angle AOB is 60 degrees, the moving point P on the arc AB is a straight line Ao parallel to Bo and Q, and the angle AOP is a. the analytic formula of the area s of the triangle poq with respect to a and the maximum value of s are obtained

I'd like to give a general introduction to the idea. Take o as the origin, OA as the x-axis to establish the coordinate system, P point coordinate is (3cosa, 3sina), straight line ob is y = root sign 3 times x (forgive me for expressing this), straight line PQ is y = root sign 3 (x-3cosa) + 3sina, Q point coordinate is 3sina-3 root sign 3 times cosa, so the expression of S can be written

There is a fan-shaped iron sheet OAB, ∠ AOB = 6O °, OA = 72cm. Cut a fan-shaped annular ABCD to make the side of the platform, and cut its inscribed circle in the remaining fan-shaped OCD
Make the bottom surface of the cone (big bottom surface), find the
(1) How long should ad take
(2) Cone volume

The inscribed circle m of sector OCD cuts arc CD to e and OA to F. connecting OE must pass m and connecting FM
Let R be the radius of the upper ground and R be the radius of the lower ground
2πR=60π×72/180
∴ R=12
In RT △ ofm
∠FOM=30°
∴OM=2R=24
∴OE=OM+R=36
∴OD=36
∴AD=OA-OD=36
∵2πr=60π×36/180
∴r=6
The height of the cone = √ 36 & # 178; - (12-6) &# 178; = 6 √ 35
The volume of round table = 6 √ 35 × (π × 6 & # 178; + π × 12 & # 178; + π × 6 × 12) / 3 = 504 π √ 35

There is a sector with a radius of 72. After cutting off a small sector OCD, the remaining sector ring ABCD is set. The sector ring area is 64, and the sector ring is rolled into the side of a cone
The difference between the upper and lower ground radii of the platform is 6, and the center angle and the height of the platform are calculated

Let the center angle be q, and according to the fan ring area 64, the countable equation is pi * 72 ^ 2 * q / 360-pi * od ^ 2 * q / 360 = 64
Secondly, the difference between the upper and lower ground radii of the round table is 6. First, the arc AB = 2 * pi * 72 * q / 360 is calculated, and then the radius after the circle is 72 * q / 360. Similarly, the upper and bottom radii od * q / 360 can be obtained, so 72 * q / 360-72 * q / 360 = 6
Two equations, two unknowns, can find out the central angle Q and OD. The simple method of calculation is the first formula after the common factor is put forward, in addition to the second formula after the common factor is put forward. Results I calculated by myself, and the height of the frustum after the previous calculation is simple, specifically: ad = oa-od, and then according to the Pythagorean theorem, H = root sign (AD ^ 2-6 ^ 2)
This 6 is the radius difference 6