Q: the perimeter ratio of the two circles is 7:4. What is the area ratio?

Q: the perimeter ratio of the two circles is 7:4. What is the area ratio?

Perimeter = 2 π R
The perimeter ratio is the radius ratio of 7:4
Area = π R & # 178;
The area ratio is 49:16

There is a round sheet of iron with a diameter of 20cm. Cut out a sector with a center angle of 90 to make a cone. What is the ground radius

Sector arc length = 20 π / 4
Let the bottom radius be r
2πr=20π/4
r=5/2

Cut a sector with a central angle of a on the circular iron sheet with radius r to make the remaining part form a cone. What is the maximum volume of the cone when a is the value?
Don't be too detailed, the general method is OK, and the word description is OK

Ice blue is right. I've calculated it. It's very complicated
Let R be the base radius of the cone and H be the height
2*pi*r=(2*pi-a)*R
So r = (2 * pi-A) * r / (2 * PI) [[1]
h^2=R^2-r^2
h＝（R^2-r^2）^0.5 【2】
Cone volume
V=1/3*pi*r^2*h 【3】
Substituting [1] and [2] into [3]
We get v = 1 / 24 / PI ^ 2 * R ^ 3 * (- 2 * PI + a) ^ 2 * (- A * (- 4 * PI + a)) ^ (1 / 2) [4]
Take the derivative of [4] and let DV / DA = 0
dV/da＝1/12/pi^2*R^3*(-2*pi+a)*(-a*(-4*pi+a))^(1/2)+1/48/pi^2*R^3*(-2*pi+a)^2/(-a*(-4*pi+a))^(1/2)*(4*pi-2*a)＝0
The solution is as follows
a =
[ 2*pi]
[ 2*pi+2/3*6^(1/2)*pi]
[ 2*pi-2/3*6^(1/2)*pi]
Obviously, a = 2 * PI and a = 2 * PI + 2 / 3 * 6 ^ (1 / 2) * PI are unreasonable
Therefore, a = 2 * pi * (1 - √ 6 / 3) ≈ 0.3670 * pi = 66.0612 degrees

If it is a side view of a cone about 7.74 cm high, calculate the volume of the cone
A quarter of a circle with a radius of 8 cm

The volume of a cylinder with equal height and equal ground is three times that of a cone
So: 8 * 8 * 3.14 * 7.74/3 = 200.96 * 7.74/3 = 518.4768

The sector with a radius of 10 cm and a central angle of 216 ° is rolled into a conical funnel. It is known that the height of the funnel is 8 cm

The circumference of the bottom surface of the cone is 10 * 216 * pi / 180 = 12pi cm, the radius is 12pi / 2pi = 6cm, and the generatrix is 10cm, so the height of the cone = root (10 * 10-6 * 6) = 8cm (the title is correct.); so the volume of the cone = 3.14 * 6 * 6 * 8 / 3 = 301.44cm3

The side view is a fan-shaped cone with a radius of 2cm and a center angle of 2 π 3. The volume of the cone is______ ．

Let the bottom radius of the cone be RCM, then the ∵ side expansion is a sector with radius length of 2cm and center angle of 2 π 3, ∵ arc length L = 2 π 3 × 2 = 4 π 3 ∵ 4 π 3 = 2 π R ∵ r = 23 ∵ cone height 4 − 49 = 432 ∵ cone volume 13 π × 49 × 432 = 162 π 81cm3, so the answer is: 162 π 81cm3

It is known that the radius of the sector AOB is 6cm, the degree of the central angle is 120 ° and if the sector is enclosed into a cone, the side area of the enclosed cone is______  cm2．

The side area of the cone is n π R & nbsp; 2360 = 12 π cm 2, so the answer is 12 π

If the side area of the cone is 12 π cm2 and its bottom radius is 3cm, then the generatrix length of the cone is______ cm．

Let the generatrix length of the cone be L. according to the meaning of the question, we get 12.2 π· 3.l = 12 π, and the solution is L = 4

It is known that the side area of the cone is 8 π cm2, and the center angle of the expanded side view is 45 degrees, then the generatrix length of the cone is 8 π cm2______ cm．

Let the generatrix length be r, the side of the cone is fan-shaped after expansion, and the side area s = 45 π, r2360 = 8 π, r = 8cm

Given that the side area of a cone is 8 π cm ^ 2, and the center angle of the expanded side view is 56 °, the generatrix length of the cone is?

The side area of a cone is equivalent to a sector, and the generatrix is equivalent to the radius of the sector
S = n π R ^ 2 / 360 = 56 π R ^ 2 / 360 = 8 π cm ^ 2, find R