Question

Спасите помогите!! По стороне основания "а" и боковому ребру "в" вычислите объем правильной четырехугольной пирамиды.

Answer 1

SАВСД - прав. четырёхугольная пирамида  ⇒  
 АВСД - квадрат со стороной а , SA=SB=SC=SД=b
 S(АВСД)=а²
Диагонали АС и ВД пересекаются в т. О . Высота SO проектируется в эту же точку О . 
ΔSOC: ∠SOC=90° , OC=0,5*AC=0,5*√(AД²+СД²)=0,5*√(а²+а²)=0,5*а√2
SO=√(SC²-OC²)=√(b²-(a²/2))=√(2b²-a²)/√2
V(SABCД)=1/3*a²*√(2b²-a²)/√2
  $V= \frac{1}{3\sqrt2} \cdot a^2\sqrt{2b^2-a^2}$

Answer 2

Calculating the Volume of a Regular Quadrilateral Pyramid

To calculate the volume of a regular quadrilateral pyramid, we can use the formula:

V = (1/3) * A_base * h

Where: - V = volume of the pyramid - A_base = area of the base - h = height of the pyramid

Finding the Area of the Base (A_base)

The area of the base of a regular quadrilateral pyramid can be calculated using the formula:

A_base = (s^2) * n

Where: - s = length of one side of the base - n = number of sides of the base (in this case, 4 for a quadrilateral base)

Calculating the Volume

Given the side length of the base "a" and the length of the lateral edge "l", we can calculate the height of the pyramid using the formula:

h = sqrt(l^2 - (a/2)^2)

Now, we can substitute the values into the volume formula to find the volume of the regular quadrilateral pyramid.

Using the Formulas to Calculate the Volume

Given the side length of the base "a" and the length of the lateral edge "l", we can calculate the volume using the formulas mentioned above.

A_base = (a^2) * 4.

h = sqrt(l^2 - (a/2)^2).

Now, we can substitute the calculated values into the volume formula:

V = (1/3) * A_base * h.

By plugging in the values for A_base and h, we can calculate the volume of the regular quadrilateral pyramid.