Question

Длина высоты правильной четырехугольной пирамиды 15см ,а периметр основания 16см .Найти V пирамиды

Answer 1

Р=16см
Н=15 см

В основании правильной четырехугольной пирамиды -  квадрат со стороной а
Р=4а
4а=16
а=4
V( пирамиды)=(1/3)·S(осн.)·H=(1/3)·a²·H=(1/3)·4²·15=80 кв. см

Answer 2

Calculation of the Volume of a Pyramid

To find the volume of a pyramid, we need to know the height and the perimeter of the base. In this case, the height of the pyramid is given as 15 cm, and the perimeter of the base is given as 16 cm.

The formula for calculating the volume of a pyramid is:

V = (1/3) * base area * height

To find the base area, we need to calculate the length of one side of the base. Since the perimeter of the base is given as 16 cm, and the base is a regular quadrilateral (four-sided polygon), we can divide the perimeter by 4 to find the length of one side of the base.

Length of one side of the base = Perimeter of the base / 4

Length of one side of the base = 16 cm / 4 = 4 cm

Now that we know the length of one side of the base, we can calculate the base area using the formula for the area of a square:

Base area = (Length of one side of the base)^2

Base area = 4 cm * 4 cm = 16 cm^2

Finally, we can substitute the values into the formula for the volume of a pyramid:

V = (1/3) * base area * height

V = (1/3) * 16 cm^2 * 15 cm

V = 80 cm^3

Therefore, the volume of the pyramid is 80 cm^3.