Given the volume 6 of a regular quadrilateral whose vertices are on the same sphere, calculate the surface area of the sphere

Given the volume 6 of a regular quadrilateral whose vertices are on the same sphere, calculate the surface area of the sphere

Let the height of a regular pyramid be h and the side length of its bottom be a,
From v = a ^ 2H / 3 = a ^ 2 = 6
So, a = √ 6
The radius of the ball can be calculated by triangle similarity
r=2,
S-sphere = 4 π R ^ 2 = 16 π

What's the center of the triangle at the bottom of the triangle?
Points, such as, three equal sides, is the outer center

If the three sides of the triangle are equal to each other, they are the inner center and the three side centers. The projection of the vertex on the bottom is not necessarily perpendicular, and the fixed point can not be determined without special cases

If the vertex a (2,3), B (- 4, - 2) and the center of gravity g (2, - 1) of △ ABC, then the coordinates of point C are

Let C (a, b)
Then the center coordinates are
2=(2-4+a)/3
-1=(3-2+b)/3
a=8
b=-4
So C (8, - 4)

The coordinates of three vertices a, B and C of △ ABC are a (2, - 1), B (1,3) and C (4, - 3.5), respectively

Using junior high school method
Make the vertical line of Y axis through B, a and C respectively, and the vertical feet are D, e and f respectively
According to the coordinates of points a, B and C
It is easy to conclude that:
BD＝1,DE＝4,AE＝2,EF＝2.5,CF＝4
therefore
S trapezoid bdfc = (1 + 4) * 6.5/2 = 16.25 (area unit)
S trapezoid bdea = (1 + 2) * 4 / 2 = 6 (area unit)
S trapezoid aefc = (2 + 4) * 2.5 / 2 = 7.5 (area unit)
So the area of △ ABC
= s trapezoid bdfc-s trapezoid bdea-s trapezoid aefc
＝16.25－6－7.5
= 2.75 (area unit)
For reference! Jiangsu Wu Yunchao wish you progress in learning

Find the approximate value. If the approximate value is equal to the exact value, is it written as approximately equal or equal
If 5 retains two decimal places 5.00, is it written as approximately equal to or equal to

Of course, it's equal. If it's completely equal, it doesn't need to be approximately equal

Mathematics Emperor help, use calculus to find the approximate value, e 0.0001 power, first aid

1

Let f (x) = the x-th power of E, what is the approximate value of F (0.1) obtained by calculus?

Linearization by differential
Take x = 0
f(0)=1-1=0
∵f'(x)=e^x
f(x)≈f(a)+f'(a)(x-a)
∴f(0.1)=f(0)+f'(0)(0.1)=0.1

Using calculus to calculate the approximate value of 10 ^ 2.03
Wrong number. Differential

It is approximately 100 + 0.03 · 100 · ln10 = 100 + 3ln10

Is the area of irregular figure calculated by calculus accurate or approximate?

The limit value is also the exact value

Approximate value calculation of advanced mathematics
Calculate the approximate value of 2.02 power of (1.04)!

2+0.02
It's equal to 2 + X
X tends to zero
I don't remember Taylor's formula
Do it by yourself. What a good idea