Question

В правильной четырехугольной пирамиде высота равна 12 см, а апофема 45 см. Найти обьем пирамиды.

Answer 1

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Answer 2

Calculation of the Volume of a Pyramid

To find the volume of a pyramid, we need to know the height and the apothem (also known as the slant height). In this case, the height of the pyramid is given as 12 cm, and the apothem is given as 45 cm.

The formula for calculating the volume of a pyramid is:

Volume = (1/3) * Base Area * Height

The base area of a four-sided pyramid is a square, and the formula for calculating the area of a square is:

Base Area = Side Length^2

To find the side length of the base, we can use the apothem and the formula for the area of a square:

Side Length = 2 * Apothem / √2

Now, let's calculate the volume of the pyramid.

1. Calculate the side length of the base: - Side Length = 2 * 45 cm / √2 - Side Length ≈ 63.64 cm

2. Calculate the base area: - Base Area = Side Length^2 - Base Area ≈ (63.64 cm)^2 - Base Area ≈ 4048.99 cm^2

3. Calculate the volume of the pyramid: - Volume = (1/3) * Base Area * Height - Volume ≈ (1/3) * 4048.99 cm^2 * 12 cm - Volume ≈ 1619.60 cm^3

Therefore, the volume of the given pyramid is approximately 1619.60 cm^3.

Please note that the calculations are approximate due to rounding.