Cube, equilateral cylinder (axis section is square), the volume of the ball is equal, their surface areas are s-positive, s-column, s-ball, then the area size is

Cube, equilateral cylinder (axis section is square), the volume of the ball is equal, their surface areas are s-positive, s-column, s-ball, then the area size is

The volume of the sphere v = 4 * π * r & # 179;
Volume of cylinder v = π * r & # 178; * 2 * r = 2 * π * r & # 179;
V-ball = v-column = = > > 4 * π * r & # 179; = 2 * π * r & # 179;
R = R * 2 to the third power
S-sphere = 4 π R & # 178;
S-column = 2 π R & # 178; + 4 π R & # 178; = 6 π R & # 178;
S-column / s-sphere = 6 π R & # 178; / 4 π R & # 178; = (6 * π * r & # 178; * 4 open cubic) / (4 * π * r & # 178;)
That is, s-column = s-ball * (27 / 2) to the third power
The volume of cube V is positive = A & # 179;
Cylinder volume v = 2 π R & # 179;
A = R * (2 π open cubic)
S positive = 6A & # 178;
S-column = 2 π R & # 178; + 4 π R & # 178; = 6 π R & # 178;
S positive / s column = 6A & # 178; / 6 π R & # 178; = R & # 178; * (4 π & # 178; open cubic) / π R & # 178; = (4 / π) open cubic
That is s-positive = s-pillar * (4 / π) open cubic
S-pillar = s-ball * (27 / 2) open cubic
(27 / 2) > 1 = = > (27 / 2) open cubic > 1
S column > s ball
S positive = s column * (4 / π) open cubic
(4 / π) > 1 = = > > (4 / π) open cubic > 1
S positive > s column
S-positive > s-pillar > s-ball

If the vertices of a cube are all on the sphere and its edge length is 2cm, then the surface area of the sphere is ()
A. 8πcm2B. 12πcm2　　C. 16πcm2　　D. 20πcm2

If the vertices of the cube are all on the sphere, then the sphere is the circumscribed sphere of the cube, then 23 = 2R, so r = 3, so the surface area of the sphere is s = 4 π R2 = 12 π cm2

The volume ratio of the inscribed sphere to the circumscribed sphere of a cube is______ ．

Let the edge length of a cube be a, then the radius of its inscribed sphere is 12a, and the radius of its circumscribed sphere is 32a, so the ratio is 1:3, so the answer is 1:3

If the total area of a cube is 24, then the volume of its circumscribed sphere is______ ．

Let the edge length of the square be a, the surface area of the inscribed cube of the ball be 24, that is, 6A2 = 24, ∩ a = 2, so the edge length of the cube is 2, the diagonal of the cube is 23, so the radius of the ball is 3, so the volume of the ball is 4 π 3r3 = 4 π 3 (3) 3 = 43 π, so the answer is 43 π

A = log (1 / 2) Tan 70 °, B = log (1 / 2) sin 25 ° and C = (1 / 2) cos 25 °
If you read it: a = one-half of log Tan 70 degree B is the same as one-half of C to the power of COS 25 degree
I'm in touch with tangled hi

Because Tan 70 ° > Tan 45 ° = 1
So a = log (1 / 2) Tan 70 degree

How to compare the size of log (4) 3 and log (3) 2
Please write down the calculation process thank you!

From the formula of changing bottom
log(4)3＝lg3/lg4
log(3)2＝lg2/lg3
therefore
log(4)3－log(3)2
＝lg3/lg4－lg2/lg3＝[(lg3)^2－lg2*lg4]/(lg4*lg3)
And because if a and B are positive numbers, then there is
[(a＋b)/2]^2－ab
＝(a^2＋2ab＋b^2)/4－ab
＝[(a－b)/2]^2≥0
So [(a + b) / 2] ^ 2 ≥ AB,
So ab ≤ [(a + b) / 2] ^ 2
So LG2 * LG4 ≤ [(LG2 + LG4) / 2] ^ 2
So (Lg3) ^ 2-lg2 * LG4
≥(lg3)^2－[(lg2＋lg4)/2]^2
＝(lg3)^2－(lg8/2)^2
＝(lg√9)^2－(lg√8)^2 ＞0
And because LG4 * Lg3 > 0
So log (4) 3 - log (3) 2 > 0
So log (4) 3 > log (3) 2

(log (3) 2 + log (9) 2) * (log (4) 3 + log (8) 3) the base number with brackets

log(9)2=0.5log(3)2(log(3)2+log(9)2)=1.5*log(3)2log(4)3=0.5log(2)3log(8)3=1/3 log(2)3log(4)3+log(8)3=5/6log(2)3(1.5*log(3)2)*(5/6log(2)3)=1.25log(3)2* log(2)3=1

Compare the size of log (1 / 2) 1 / 3 and log (1 / 3) 1 / 2

The former is LG (1 / 3) / LG (1 / 2) and the latter is LG (1 / 2) / LG (1 / 3). Because LG increases at (0,1) and is always less than 0, the former is more than 1 and the latter is log (1 / 3) 1 / 2

The number in the first bracket after log is the base
Log (2)

1 / 16 = 2 (- 4) power, 1 / 16 cube root = 2 (- 4 / 3) power, do you understand? The original formula = log with 2 as the base (2-4 / 3 power × 2-4 / 6 power) = log with 2 as the base (2-4 / 6 power) = 2 / 3

If log is based on 2 [log is based on 3 (log is based on 4, x)] = 0, then x=
Please answer in detail, thank you!

Log base 3 (log base 4, x) = 2 ^ 0 = 1
Log is based on 4, x = 3 ^ 1 = 3
x=4^3=64