Let the total area of a cube be 24cm2 and a sphere be inscribed to the cube, then the surface area of the sphere is______ ．

Let the total area of a cube be 24cm2 and a sphere be inscribed to the cube, then the surface area of the sphere is______ ．

If the total area of the cube is 24cm2, the edge length of the cube is 2cm, and the sphere is inscribed on the cube, the diameter of the sphere is 2cm, then the radius of the sphere is 1m, and the surface area of the sphere is S4 π R2 = 4 π cm3, so the answer is: 4 π cm3

If the total area of a cube is known to be a, then the volume of the circumscribed sphere of the cube is a

Let the edge length of a cube be l, then there are: 6L & # 178; = a
The solution is: l = radical (A / 6) = [radical (6a)] / 6
And the diameter of the circumscribed ball of the cube is the diagonal length of the cube
So the diameter of the circumscribed ball 2R = radical 3 * [radical (6a)] / 6 = [radical (2a)] / 2
That is radius r = [radical (2a)] / 4
So the volume of circumscribed sphere = (4 / 3) * π * r & # 179;
=(4 / 3) * π * {[radical (2a)] / 4} & # 179;
=(radical 2) * π * a * (radical a) / 8

If the volume of the inscribed sphere of a cube is 36 π, what is the surface area of the cube

According to your question, the answers are as follows:
Let the radius of the inscribed sphere be r, the diameter be D, the volume be V, the side length of the cube be l, and the surface area be s
According to the volume formula of the sphere v = 4 / 3 π r?, and we know that the volume of the inscribed sphere is v = 36 π, so 4 / 3 π r? = 36 π, so r? = 27, the radius of the inscribed sphere r = 3, and the diameter D = 2R = 6. Because the diameter of the inscribed sphere of the cube is equal to the side length of the cube, and the side length of the cube L = D = 6, the area of each face of the cube is 6? = 36, and the cube has six faces, so the surface area of the cube s = 36 * 6 = 216

If we know that the surface area of the frontal body is 4, the volume of the tetrahedron is 3_______ .
.

Strengthen drawing. Draw a picture, at a glance
It can be calculated that the height is root 6 / 3
Then calculate the volume
=1 / 3 * root 3 (bottom area) * root 6 / 3 (height)
=Root 2 / 3

Image constant crossing point a of function y = log (x + 3) - 1

Image constant crossing point a with y = log (x + 3) - 1
x+3=1；x=-2；
y=-1；
A（-2,-1）
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How to draw the image of y = log | x + 2 | and y = log | x |

The image of y = LG (x) can be obtained by image transformation
(1) Y = LG | x |, the image of y = LG (x) is reserved, and then the image symmetrical with the right image about y axis is added on the left side of Y axis
(2) Move the image of y = LG | x | 2 units to the left

Let log (base 2) 3 = m, then what is the value of log (base 3) 4?

Log (base 2) 3 = M = = > Lg3 / LG2 = M = = > LG2 / Lg3 = 1 / M = = > 2lg2 / Lg3 = 2 / M = = > LG4 / Lg3 = 2 / M = = > log (base 3) 4 = 2 / M

Given log (2) [log (3) (log (4) x)] = log (3) [log (4) (log (2) y)] = 0, find the value of X + y

log（2)[log（3)(log(4) x)] = 0
log（3)(log(4) x) = 1
log(4) x = 3
x = 64
log(3)[log(4) (log(2) y)] = 0
log(4)(log(2) y) = 1
log(2) y = 4
y = 16
So x + y = 80

Log (3) m + log (3) n = 4

The sum of the logarithms with the same base equals to the multiplication of the true number, so it is equal to log (3) Mn = 4, so the fourth power of Mn equal to 3 is equal to 81, and then when m + n is greater than or equal to 2 times of the root sign of the basic inequality, M + n equals 18

Find the value of m when log (2) 3 * log (3) 4 * log (4) 5 * log (5) 6 * log (6) 7 * log (7) M = log (3) 9?

log(2)3*log(3)4*log(4)5*log(5)6*log(6)7*log(7)m=log(3)9
According to the bottom formula
lg3/lg2*lg4/lg3*lg5/lg4*lg6/lg5*lg7/lg6*lgm/lg7=2
lgm/lg2=2
lgm=2lg2=lg4
m=4