Question

В основании правильной пирамиды лежит квадрат со стороной 10 см высота 12 см найти площадь поверхности и обьём пирамиды»

Answer 1

Пишите, если что не так

Answer 2

Calculating the Surface Area and Volume of a Pyramid

To find the surface area and volume of a pyramid, we can use the following formulas:

1. Surface Area (A): The surface area of a pyramid can be calculated using the formula: A = 0.5 * Perimeter of the base * Slant height + Base area.

2. Volume (V): The volume of a pyramid can be calculated using the formula: V = (1/3) * Base area * Height.

Given: - Base: Square with a side length of 10 cm. - Height: 12 cm.

Calculating the Surface Area:

The first step is to calculate the slant height of the pyramid. The slant height (l) can be found using the Pythagorean theorem, where l^2 = h^2 + (0.5 * side length)^2.

Using the given values: - h = 12 cm - Side length = 10 cm

We can calculate the slant height (l) using the formula l = sqrt(h^2 + (0.5 * side length)^2).

Calculating the slant height: l^2 = 12^2 + (0.5 * 10)^2 l^2 = 144 + 25 l^2 = 169 l = sqrt(169) l = 13 cm

Now that we have the slant height, we can calculate the surface area using the formula: A = 0.5 * Perimeter of the base * Slant height + Base area.

The perimeter of the base is 4 * side length, and the base area is side length^2.

Calculating the Volume:

The volume of the pyramid can be calculated using the formula: V = (1/3) * Base area * Height.

The base area is side length^2.

Now, let's calculate the surface area and volume using the given values and the formulas above.

Results:

- Surface Area (A): A = 0.5 * 4 * 10 * 13 + 10^2 = 0.5 * 40 * 13 + 100 = 260 + 100 = 360 cm^2. - Volume (V): V = (1/3) * 10^2 * 12 = (1/3) * 100 * 12 = 400 cm^3.

So, the surface area of the pyramid is 360 cm^2, and the volume of the pyramid is 400 cm^3.