The radius of the big circle is six times that of the small circle, and the circumference of the small circle is six times that of the big circle______ The area of a large circle is the area of a small circle______ ．

The radius of the big circle is six times that of the small circle, and the circumference of the small circle is six times that of the big circle______ The area of a large circle is the area of a small circle______ ．

Let the radius of the small circle be r, then the radius of the large circle be 6R, the perimeter of the small circle be 2 π R, the perimeter of the large circle be 2 π × 6R = 12 π R, 12 π R △ 2 π r = 6 times; the area of the small circle be π R2, the area of the large circle be π (6R) 2 = 36 π R2, 36 π R2 △ π R2 = 36 times

The radius of the small circle is one third of the radius of the large circle, the perimeter ratio of the large circle to the small circle is (), and the area ratio of the small circle to the large circle is ()

The radius of the small circle is one third of the radius of the large circle, the perimeter ratio of the large circle to the small circle is (3:1), and the area ratio of the small circle to the large circle is (1:9)

The height of the cone is 10cm, and the side view is semicircle. What is the side area of the cone? What is the vertex angle of the isosceles triangle with axial section?

Let R be the base radius of the cone
Then 2 π r = π √ (10 ^ 2 + R ^ 2)
R = 10 / √ 3cm
The lateral area is: π * (10 ^ 2 + R ^ 2) / 2 = 200 π / 3 square centimeter
The vertex angle is: 2arctan (R / 10) = 60 degrees

The radius of the bottom of the cone is 10 cm, and the cross section of the contour line is an isosceles triangle with a vertex angle of 60 degrees. (1) calculate the height of the cone. (2) calculate the height of the cone

An isosceles triangle with a vertex angle of 60 ° is an equilateral triangle
(1) The diameter of the cone is 20 and the length of the generatrix is 20,
The height is 10 * √ 3
(2) The area (sector) of the expanded side view of the cone is s = 1 / 2 × arc length × radius. (Note: This is the sector radius, i.e. the generatrix length, and the arc length is the perimeter of the bottom area of the cone.)
S=1/2*(20*3.14)*20=628

The height of a cone is h, the side view is semicircle, and the side area of a cone is
There should be an explanation

Let the semicircle radius r, then the radius of the bottom circle is the root sign (R ^ 2-h ^ 2)
The circumference of the ground circle is 2 times Π times the root sign (R ^ 2-h ^ 2) = the arc length of the semicircle Π R
The solution is R ^ 2 = 4 / 3H ^ 2
Side area s = 1 / 2 Π R ^ 2 = 2 / 3 Π H ^ 2

It is known that the height of a cone is 3 and its side expansion is semicircle. The side area and volume of the cone are calculated

Let the radius of the bottom circle of the cone be r, and the radius of the side half circle be r. obviously, if the circumference of the bottom circle of the cone is equal to the arc length of the side half circle, then there is 2 π r = (1 / 2) x 2 π r = π R, that is, r = 2R

It is known that the surface area of a cone is a square meter, and the expanded side area of the cone is a semicircle

Let R be the base radius of the cone
Then, the perimeter of the bottom circle is 2 π R and the area is π R ^ 2
Its side area expansion is a semicircle
The length of the semicircle is 2 π R, so the radius of the semicircle is 2R
So the area of the semicircle is 0.5 * π * (2R) ^ 2
So a = 0.5 * π * (2R) ^ 2 + π R ^ 2 = 3 π R ^ 2
So r = under the radical (A / 3 π)

The central angle of the sector is 120 degrees and the area is 30 π square centimeter. If the sector is rolled into a cone, the volume of the cone can be calculated

r^2=30pi/(2pi/3)=90;
r=sqrt(90);
The radius of the winding cone is sqrt (10), the height is 4 * sqrt (5), and the thickness is 5;
So volume = (1 / 3) pi * sqrt (10) * sqrt (10) * 4 * sqrt (5) = (40sqrt (5) / 3) PI

If the central angle of a cone's side view is 120 °, the ratio of its side area to its surface area is___ ．

The arc length of ∵ fan is 120 × π R180, the circumference of the bottom circle of cone is 2 π R, ∵ 120 × π R180 = 2 π R, RR = 31, we can get the following formula: cone generatrix L = R, ∵ side area formula of cone: S = π RL, surface area: π RL + π R2 = 4 π R2, ∵ side area: π RL = 3 π R2, ∵ the ratio of side product to surface area is 34

If the surface area of the cone is 16 π and the center angle of the side view is 120 °, then the volume of the cone is___ ．

Let R be the base radius of the cone, l be the generatrix, and 120 ° be the center angle of the side expanded view, so 2 π r = 2 π 3l, l = 3R, s = π R2 + π R · 3R = 4 π R2 = 16 π, r = 2, H = l2-r2 = 36-4 = 42V = 13 π r2h = 13 π × 4 × 42 & nbsp; = 1623 π, so the answer is: 1623 π